Atomic orbital - Knowledge

8590:. To see the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average drum membrane velocity and momentum at that point) must be considered relative to that point's distance from the center of the drum head. If this displacement is taken as being analogous to the probability of finding an electron at a given distance from the nucleus, then it will be seen that the many modes of the vibrating disk form patterns that trace the various shapes of atomic orbitals. The basic reason for this correspondence lies in the fact that the distribution of kinetic energy and momentum in a matter-wave is predictive of where the particle associated with the wave will be. That is, the probability of finding an electron at a given place is also a function of the electron's average momentum at that point, since high electron momentum at a given position tends to "localize" the electron in that position, via the properties of electron wave-packets (see the 3461: 1359:

space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus the binding energy to contain or trap a particle in a smaller region of space increases without bound as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require infinite particle momentum.

1283:, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength. The Bohr model for a short time could be seen as a classical model with an additional constraint provided by the 'wavelength' argument. However, this period was immediately superseded by the full three-dimensional wave mechanics of 1926. In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed. 2846: 8574: 5435: 3456:{\displaystyle \psi _{n,\ell ,m}^{\text{real}}={\begin{cases}{\sqrt {2}}(-1)^{m}{\text{Im}}\left\{\psi _{n,\ell ,|m|}\right\}&{\text{ for }}m<0\\\psi _{n,\ell ,|m|}&{\text{ for }}m=0\\{\sqrt {2}}(-1)^{m}{\text{Re}}\left\{\psi _{n,\ell ,|m|}\right\}&{\text{ for }}m>0\end{cases}}={\begin{cases}{\frac {i}{\sqrt {2}}}\left(\psi _{n,\ell ,-|m|}-(-1)^{m}\psi _{n,\ell ,|m|}\right)&{\text{ for }}m<0\\\psi _{n,\ell ,|m|}&{\text{ for }}m=0\\{\frac {1}{\sqrt {2}}}\left(\psi _{n,\ell ,-|m|}+(-1)^{m}\psi _{n,\ell ,|m|}\right)&{\text{ for }}m>0\\\end{cases}}} 7351: 4992: 6796: 857: 7137: 9250: 9187: 9124: 8914: 8851: 8788: 1759: 10183: 367: 8084: 8077: 12787: 8070: 10156: 12797: 5430:{\displaystyle {\begin{aligned}\psi _{n,1,-1}^{\text{real}}=&n{\text{p}}_{y}={\frac {i}{\sqrt {2}}}\left(n{\text{p}}_{-1}+n{\text{p}}_{+1}\right)\\\psi _{n,1,0}^{\text{real}}=&n{\text{p}}_{z}=2{\text{p}}_{0}\\\psi _{n,1,+1}^{\text{real}}=&n{\text{p}}_{x}={\frac {1}{\sqrt {2}}}\left(n{\text{p}}_{-1}-n{\text{p}}_{+1}\right)\\\psi _{n,3,+1}^{\text{real}}=&nf_{xz^{2}}={\frac {1}{\sqrt {2}}}\left(nf_{-1}-nf_{+1}\right)\end{aligned}}} 1227: 7948: 40: 10370:"blocks", is more obvious if this order of filling is given in matrix form, with increasing principal quantum numbers starting the new rows ("periods") in the matrix. Then, each subshell (composed of the first two quantum numbers) is repeated as many times as required for each pair of electrons it may contain. The result is a compressed periodic table, with each entry representing two successive elements: 8063: 8056: 8049: 7941: 7934: 7927: 7851: 7844: 9394: 9356: 9318: 9086: 9048: 9010: 8750: 8712: 8674: 8157: 8035: 8021: 4589: 8319: 8216: 8209: 8150: 8143: 8136: 8129: 8108: 8101: 8042: 8028: 8014: 8007: 7986: 7979: 7920: 7899: 7892: 7837: 7830: 7783: 8230: 8223: 8122: 8115: 8000: 7993: 7913: 7906: 1182:, but were rather composite particles. The newly discovered structure within atoms tempted many to imagine how the atom's constituent parts might interact with each other. Thomson theorized that multiple electrons revolve in orbit-like rings within a positively charged jelly-like substance, and between the electron's discovery and 1909, this " 10185: 10189: 10188: 10184: 10190: 880:(i.e., atom with one electron). Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron (i.e., orbitals) but are used as starting points for approximating wave functions that depend on the simultaneous coordinates of all the electrons in an atom or molecule. The 1254:

of atoms became an increasingly useful tool in the understanding of electrons in atoms. The most prominent feature of emission and absorption spectra (known experimentally since the middle of the 19th century), was that these atomic spectra contained discrete lines. The significance of the Bohr model

1193:

predicted a different model for electronic structure. Unlike the plum pudding model, the positive charge in Nagaoka's "Saturnian Model" was concentrated into a central core, pulling the electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time,

11114:

will be absorbed by the electron in state 1, and that electron will jump to state 2. However, photons that are greater or lower in energy cannot be absorbed by the electron, because the electron can jump only to one of the orbitals, it cannot jump to a state between orbitals. The result is

10720:

atoms. This relativistic increase in momentum for high speed electrons causes a corresponding decrease in wavelength and contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electrons in lighter elements in the same column of the periodic table); this results in

7287:

look similar, each with four pear-shaped lobes, each lobe tangent at right angles to two others, and the centers of all four lying in one plane. Three of these planes are the xy-, xz-, and yz-planes—the lobes are between the pairs of primary axes—and the fourth has the center along the x and y axes

6826:

Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero

444:

Thus, electrons cannot be described simply as solid particles. An analogy might be that of a large and often oddly shaped "atmosphere" (the electron), distributed around a relatively tiny planet (the nucleus). Atomic orbitals exactly describe the shape of this "atmosphere" only when one electron is

1378:

which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a

8999:

orbitals are necessary to localize a particle with angular momentum and a wave nature in an orbital where it must tend to stay away from the central attraction force, since any particle localized at the point of central attraction could have no angular momentum. For these modes, waves in the drum

7302:

values higher than the lowest possible value, exhibit an additional radial node structure which is reminiscent of harmonic waves of the same type, as compared with the lowest (or fundamental) mode of the wave. As with s orbitals, this phenomenon provides p, d, f, and g orbitals at the next higher

7235:

crystal using scanning transmission electron microscopy with energy dispersive x-ray spectroscopy. Because the imaging was conducted using an electron beam, Coulombic beam-orbital interaction that is often termed as the impact parameter effect is included in the outcome (see the figure at right).

3802:

Real spherical harmonics are physically relevant when an atom is embedded in a crystalline solid, in which case there are multiple preferred symmetry axes but no single preferred direction. Real atomic orbitals are also more frequently encountered in introductory chemistry textbooks and shown in

1358:

implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself. In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in

10278:

Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose

1161:

published an orbit-based hypothesis for electron behavior as early as 1904. These theories were each built upon new observations starting with simple understanding and becoming more correct and complex. Explaining the behavior of these electron "orbits" was one of the driving forces behind the

1126:

Although hydrogen-like orbitals are still used as pedagogical tools, the advent of computers has made STOs preferable for atoms and diatomic molecules since combinations of STOs can replace the nodes in hydrogen-like orbitals. Gaussians are typically used in molecules with three or more atoms.

9734:

The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron–electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less

1741:

Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers. These quantum numbers occur only in certain combinations of values, and their physical interpretation changes depending on whether

4403: 10949:

Bound quantum states have discrete energy levels. When applied to atomic orbitals, this means that the energy differences between states are also discrete. A transition between these states (i.e., an electron absorbing or emitting a photon) can thus happen only if the photon has an energy

11121:

The atomic orbital model is nevertheless an approximation to the full quantum theory, which only recognizes many electron states. The predictions of line spectra are qualitatively useful but are not quantitatively accurate for atoms and ions other than those containing only one electron.

445:

present. When more electrons are added, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ("electron cloud") tends toward a generally spherical zone of probability describing the electron's location, because of the

7370:(e.g., all three 2p orbitals, or all five 3d orbitals) where each orbital is occupied by an electron or each is occupied by an electron pair, then all angular dependence disappears; that is, the resulting total density of all the atomic orbitals in that subshell (those with the same 10187: 10191: 4835: 1210:

discovered that the bulk of the atomic mass was tightly condensed into a nucleus, which was also found to be positively charged. It became clear from his analysis in 1911 that the plum pudding model could not explain atomic structure. In 1913, Rutherford's post-doctoral student,

8609: orbitals in an atom. This antinode means the electron is most likely to be at the physical position of the nucleus (which it passes straight through without scattering or striking it), since it is moving (on average) most rapidly at that point, giving it maximal momentum. 335:(or electron cloud or wave mechanics model), a modern framework for visualizing submicroscopic behavior of electrons in matter. In this model electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler 839:

Fundamentally, an atomic orbital is a one-electron wave function, even though many electrons are not in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital visualization heavily influenced by the

8979:

orbitals in an atom. These orbitals all have some angular momentum, and in the planetary model, they correspond to particles in orbit with eccentricity less than 1.0, so that they do not pass straight through the center of the primary body, but keep somewhat away from it.

7222:, each single s orbital is made of spherically symmetric surfaces which are nested shells (i.e., the "wave-structure" is radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right. The s orbitals for all 1334: = 2 in neon. In argon, the 3s and 3p subshells are similarly fully occupied by eight electrons; quantum mechanics also allows a 3d subshell but this is at higher energy than the 3s and 3p in argon (contrary to the situation for hydrogen) and remains empty. 1263:

was not suggested until eleven years later. Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step toward the understanding of electrons in atoms, and also a significant step towards the development of

1194:

and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation. Nevertheless, the

11098:. If the electron receives energy that is less than or greater than this value, it cannot jump from state 1 to state 2. Now, suppose we irradiate the atom with a broad-spectrum of light. Photons that reach the atom that have an energy of exactly 11635:"On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure" 7140:

Experimentally imaged 1s and 2p core-electron orbitals of Sr, including the effects of atomic thermal vibration and excitation broadening, retrieved from energy dispersive x-ray spectroscopy (EDX) in scanning transmission electron microscopy

3735: 831:

and cannot be distinguished from each other. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinant wave function at all. This is the case when

4332: 9614:

In atoms with multiple electrons, the energy of an electron depends not only on its orbital, but also on its interactions with other electrons. These interactions depend on the detail of its spatial probability distribution, and so the

9818:

given by its row and column indices, respectively. The number in the cell is the subshell's position in the sequence. For a linear listing of the subshells in terms of increasing energies in multielectron atoms, see the section below.

8635:

Below, a number of drum membrane vibration modes and the respective wave functions of the hydrogen atom are shown. A correspondence can be considered where the wave functions of a vibrating drum head are for a two-coordinate system

10875:

is about 173. These conditions are not seen except transiently in collisions of very heavy nuclei such as lead or uranium in accelerators, where such electron-positron production from these effects has been claimed to be observed.

3578: 7226:

numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node

4584:{\displaystyle {\begin{aligned}\psi _{n,1,+1}^{\text{real}}=&R_{n,1}{\sqrt {\frac {3}{4\pi }}}\cdot {\frac {x}{r}}\\\psi _{n,1,-1}^{\text{real}}=&R_{n,1}{\sqrt {\frac {3}{4\pi }}}\cdot {\frac {y}{r}}\end{aligned}}} 1613:

down to a single electron (He, Li, etc.) is very similar to hydrogen, and the orbitals take the same form. In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the

10674:

Although this is the general order of orbital filling according to the Madelung rule, there are exceptions, and the actual electronic energies of each element are also dependent upon additional details of the atoms (see

823:. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless, one has to keep in mind that electrons are 10812:

is the speed of light. In non-relativistic quantum mechanics, therefore, any atom with an atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light. Even in the

10186: 1294: = 1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that 5569:

Below is a list of these Cartesian polynomial names for the atomic orbitals. There does not seem to be reference in the literature as to how to abbreviate the long Cartesian spherical harmonic polynomials for

1561:

The superscript y shows the number of electrons in the subshell. For example, the notation 2p indicates that the 2p subshell of an atom contains 4 electrons. This subshell has 3 orbitals, each with n = 2 and

4690: 1680:) of a hydrogen-like atom are its atomic orbitals. However, in general, an electron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending "mixtures" ( 11115:

that only photons of a specific frequency will be absorbed by the atom. This creates a line in the spectrum, known as an absorption line, which corresponds to the energy difference between states 1 and 2.

435:

Electrons retain particle-like properties such as: each wave state has the same electric charge as its electron particle. Each wave state has a single discrete spin (spin up or spin down) depending on its

4682: 383:

and experimental findings (such as the two slit diffraction of electrons), it was found that the electrons orbiting a nucleus could not be fully described as particles, but needed to be explained by

7386:

This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to

4070: 370:

Cross-sections of atomic orbitals of the electron in a hydrogen atom at different energy levels. The probability of finding the electron is given by the color, as shown in the key at upper right.

10716:, the effects of relativity become more pronounced, and especially so for s electrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high- 4997: 4408: 4007: 1223:

of the atom fixed the problem of energy loss from radiation from a ground state (by declaring that there was no state below this), and more importantly explained the origin of spectral lines.

10146:

Note: empty cells indicate non-existent sublevels, while numbers in italics indicate sublevels that could (potentially) exist, but which do not hold electrons in any element currently known.

4180: 2841: 2627: 2095: 7133:

of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the size of the atom remains very roughly constant, even as the number of electrons increases.

4395: 2000:, describes the projection of the orbital angular momentum along a chosen axis. It determines the magnitude of the current circulating around that axis and the orbital contribution to the 8975:

None of the other sets of modes in a drum membrane have a central antinode, and in all of them the center of the drum does not move. These correspond to a node at the nucleus for all non-

6783: 6509: 6721: 1215:, proposed a new model of the atom, wherein electrons orbited the nucleus with classical periods, but were permitted to have only discrete values of angular momentum, quantized in units 10692:, tend to be responsible for an element's chemical behavior. Elements that contain the same number of valence electrons can be grouped together and display similar chemical properties. 9304: 9241: 9178: 8968: 8905: 1784:. In fact, it can be any positive integer, but for reasons discussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated with each value of 10290:. The table may be divided into several rows (called 'periods'), numbered starting with 1 at the top. The presently known elements occupy seven periods. If a certain period has number 8842: 6008: 5949: 5890: 5797: 5738: 5679: 6416: 1555: 1864: 2574:

states that no two electrons in an atom can have the same values of all four quantum numbers. If there are two electrons in an orbital with given values for three quantum numbers, (

1370:, Mulliken and others noted that the consequence of Heisenberg's relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. 10863:

due to the non-point-charge nature of the nucleus and very small orbital radius of inner electrons, resulting in a potential seen by inner electrons which is effectively less than

8564: 3982: 1442: 6662: 6585: 1584:, which is a continuation of the notations used before orbital theory was well understood. In this system, the principal quantum number is given a letter associated with it. For 6622: 6333: 9591:

are degenerate in the Schrödinger approximation, and have the same energy. This approximation is broken slightly in the solution to the Dirac equation (where energy depends on

3903: 2737: 1120: 8567: 7292:

in between two pear-shaped regions placed symmetrically on its z axis. The overall total of 18 directional lobes point in every primary axis direction and between every pair.

6545: 1766:

In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure

1685: 1645:

similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, numerical approximations must be used.

7001:

wavelength around the circumference. Although rarely shown, the traveling wave solutions can be seen as rotating banded tori; the bands represent phase information. For each

6366: 6296: 6263: 5564: 5532: 415:. The electron's charge acts like it is smeared out in space in a continuous distribution, proportional at any point to the squared magnitude of the electron's wave function. 8520: 6195: 6165: 6135: 5500: 5471: 2686: 2657: 3797: 1066: 1255:

was that it related the lines in emission and absorption spectra to the energy differences between the orbits that electrons could take around an atom. This was, however,

922:

in polyatomic molecules. The advantage of spherical coordinates here is that an orbital wave function is a product of three factors each dependent on a single coordinate:

10776: 5831: 2218: 1641:

For atoms with two or more electrons, the governing equations can be solved only with the use of methods of iterative approximation. Orbitals of multi-electron atoms are

9249: 9186: 9123: 8913: 8850: 8787: 6066: 5594: 3765: 3622: 3617: 2125: 2053: 1998: 1153:

explained around 1913 that electrons might revolve around a compact nucleus with definite angular momentum. Bohr's model was an improvement on the 1911 explanations of

804:

and usually associated with particular electron configurations, i.e., by occupation schemes of atomic orbitals (for example, 1s 2s 2p for the ground state of

10841: 8601: orbitals (the top row in the animated illustration below), it can be seen that the very center of the drum membrane vibrates most strongly, corresponding to the 10800: 9729: 9703: 7202: 6447: 6228: 6101: 6037: 4189: 2495: 1956: 1930: 1897: 9424: 9386: 9348: 9116: 9078: 9040: 8780: 8742: 8704: 9816: 9753: 9677: 9657: 9569: 4984: 4110: 3923: 3841: 2443: 2403: 2026: 703: 616: 265: 9489: 8484: 4924: 2469: 12837: 9000:

head tend to avoid the central point. Such features again emphasize that the shapes of atomic orbitals are a direct consequence of the wave nature of electrons.

8597:

This relationship means that certain key features can be observed in both drum membrane modes and atomic orbitals. For example, in all of the modes analogous to

351:

arises naturally from total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number

9796: 9773: 9637: 9589: 9549: 9529: 9509: 9463: 5614: 4964: 4944: 4898: 4878: 4858: 4130: 4090: 3861: 3821: 2797: 2777: 2757: 2423: 2383: 676: 656: 589: 569: 545: 11082:. Now, what would happen if an electron in state 1 were to move to state 2? For this to happen, the electron would need to gain an energy of exactly 10306:

in the properties of the elements might be explained by the periodic filling of the electron energy levels, resulting in the electronic structure of the atom.

411:

The electrons are never in a single point location, though the probability of interacting with the electron at a single point can be found from the electron's

3468: 2600:

direction in Cartesian coordinates), and they also imply a preferred direction along this preferred axis. Otherwise there would be no sense in distinguishing

10871: value, which makes the atom unstable with regard to high-field breakdown of the vacuum and production of electron-positron pairs, does not occur until 2445:

is represented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, one may speak of the subshell with

9705:, the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s orbital in the next higher shell; when 1390:

in a three-dimensional atom and was pictured as the most probable energy of the probability cloud of the electron's wave packet which surrounded the atom.

12944: 11118:

The atomic orbital model thus predicts line spectra, which are observed experimentally. This is one of the main validations of the atomic orbital model.

202:). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of 7358:

Although individual orbitals are most often shown independent of each other, the orbitals coexist around the nucleus at the same time. Also, in 1927,

6957:

graphs, but have the same number of lobes in the same places, and otherwise are recognizable. This article, to show wave function phase, shows mostly

2700:, real orbitals are related to complex orbitals in the same way that the real spherical harmonics are related to complex spherical harmonics. Letting 769:.) A state is actually a function of the coordinates of all the electrons, so that their motion is correlated, but this is often approximated by this 13069: 8991:

modes in an atom show spatial irregularity along the different radial directions from the center of the drum, whereas all of the modes analogous to

12282: 11214: 1669:. The rules restricting the values of the quantum numbers, and their energies (see below), explain the electron configuration of the atoms and the 9778:

The energy sequence of the first 35 subshells (e.g., 1s, 2p, 3d, etc.) is given in the following table. Each cell represents a subshell with

9393: 9355: 9317: 9085: 9047: 9009: 8749: 8711: 8673: 10177:

from the nucleus). These images are faithful to the angular component of the orbital, but not entirely representative of the orbital as a whole.

5444:

which is favored by quantum physicists. Other conventions exist for the phase of the spherical harmonics. Under these different conventions the

761:) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their 12022:

Blanco, Miguel A.; Flórez, M.; Bermejo, M. (December 1997). "Evaluation of the rotation matrices in the basis of real spherical harmonics".

9731:

the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have been filled.

6847:

has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour. Although

1246:

to relate energy levels in atoms with the wavelength of emitted light, the connection between the structure of electrons in atoms and the

12830: 10676: 4946:. We then use the abbreviated polynomial as a subscript label for the atomic state, using the same nomenclature as above to indicate the 4830:{\displaystyle \psi _{n,3,+1}^{\text{real}}=R_{n,3}{\frac {1}{4}}{\sqrt {\frac {21}{2\pi }}}\cdot {\frac {x\cdot (5z^{2}-r^{2})}{r^{3}}}} 12130:"Probing core-electron orbitals by scanning transmission electron microscopy and measuring the delocalization of core-level excitations" 9607: electrons that go nearer the nucleus, since these feel a very slightly different nuclear charge, even in one-electron atoms; see 11697: 11527: 6827:

probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or

12939: 10344:

The following is the order for filling the "subshell" orbitals, which also gives the order of the "blocks" in the periodic table:

1127:

Although not as accurate by themselves as STOs, combinations of many Gaussians can attain the accuracy of hydrogen-like orbitals.

328:

continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between letters "i" and "j".

12682: 4597: 819:

expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated with a given

12965: 12823: 9551:, the energy becomes so high that the electron can easily escape the atom. In single electron atoms, all levels with different 1259:

achieved by Bohr through giving the electrons some kind of wave-like properties, since the idea that electrons could behave as

12239:

Cazenave, Lions, T., P.; Lions, P. L. (1982). "Orbital stability of standing waves for some nonlinear Schrödinger equations".

13307: 13062: 12598: 12579: 12560: 12537: 12466: 12006: 11981: 11956: 11836: 11680: 11586: 11375: 11350: 11323: 11298: 11267: 11242: 10904: 10325:-state depends upon the period). For instance, the leftmost two columns constitute the 's-block'. The outermost electrons of 10283:) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above. 217: 11232: 10879:

There are no nodes in relativistic orbital densities, although individual components of the wave function will have nodes.

10313:'. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same 4012: 11436:

Mulliken, Robert S. (July 1932). "Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations".

7060:

are surfaces on which the probability density vanishes. The number of nodal surfaces is controlled by the quantum numbers

1477:

For example, the orbital 1s (pronounced as the individual numbers and letters: "'one' 'ess'") is the lowest energy level (

1015:

which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons:

11172: 11132: 8439:

For the elements whose highest occupied orbital is a 6d orbital, only some electronic configurations have been confirmed.

3987: 10927:; the 9s subshell should also participate, as these elements are expected to be analogous to the respective 5p elements 12057: 11931: 11906: 10215:). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the 13100: 12872: 12518: 11424:

Therefore, the wave function of a system of identical interacting particles must not distinguish among the particles.

11417: 4138: 2802: 2100:

The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of

2058: 770: 13055: 7270:

are oriented at right angles to each other, as determined by their respective linear combination of values of

4840:

In all these cases we generate a Cartesian label for the orbital by examining, and abbreviating, the polynomial in

4337: 11698:"Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity" 11528:"Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity" 6727: 6453: 11670: 6668: 1467: 742: 355:, particularly when the atom bears a positive charge, energies of certain sub-shells become very similar and so, 310: 9258: 9195: 9132: 8922: 8859: 10701: 8796: 5955: 5896: 5837: 5744: 5685: 5626: 5441: 2697: 1268:

in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.

17: 11739:

Heisenberg, W. (March 1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik".

9755:

of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers

6372: 3767:

is the real spherical harmonic related to either the real or imaginary part of the complex spherical harmonic

2692:

Instead of the complex orbitals described above, it is common, especially in the chemistry literature, to use

1515: 13338: 12727: 8587: 1824: 1804:

describes the orbital angular momentum of each electron and is a non-negative integer. Within a shell where

12643: 10220: 8525: 7307:(for example, 3p orbitals vs. the fundamental 2p), an additional node in each lobe. Still higher values of 4183: 2615: 2525: 1605:

The simplest atomic orbitals are those that are calculated for systems with a single electron, such as the

1275:'s suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 464:

weights. So, for instance, an electron could be in a state (2, 1, 0), a pure eigenstate, or a mixed state

9679:

are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When

7375: 7231:

the nucleus). Recently, there has been an effort to experimentally image the 1s and 2p orbitals in a SrTiO

7098:

on the quantum numbers. The principal quantum number controls the total number of nodal surfaces which is

3928: 2696:

atomic orbitals. These real orbitals arise from simple linear combinations of complex orbitals. Using the

1409: 12675: 11203: 10728:(which results from 6s electrons not being available for metal bonding) and the golden color of gold and 7047:

there are no counter rotating modes. There are only radial modes and the shape is spherically symmetric.

6628: 6551: 1622:

for the energy. They can be obtained analytically, meaning that the resulting orbitals are products of a

904: 11741: 8573: 6591: 6302: 13378: 12109: 10944: 10924: 7362:

proved that if one sums the electron density of all orbitals of a particular azimuthal quantum number

3869: 2703: 1085: 1023:

are derived from the exact solutions of the Schrödinger equation for one electron and a nucleus, for a

820: 789: 6515: 2614:. As such, the model is most useful when applied to physical systems that share these symmetries. The 705:

would definitely be 1. Eigenstates make it easier to deal with the math. You can choose a different

456:

of an electron in its orbit. An actual electron exists in a superposition of states, which is like a

13368: 13328: 13312: 12960: 12713: 10216: 9445:), the energy of an orbital (and, consequently, any electron in the orbital) is determined mainly by 8995: modes are perfectly symmetrical in radial direction. The non-radial-symmetry properties of non- 7266:"—there are two lobes pointing in opposite directions from each other). The three p orbitals in each 6339: 6269: 6236: 5537: 5505: 2571: 2005: 1699:

where it determines the radius of each circular electron orbit. In modern quantum mechanics however,

1311: 828: 816: 746: 384: 12495: 12301: 11854: 11634: 10724:

Examples of significant physical outcomes of this effect include the lowered melting temperature of

8489: 6815:

hydrogen orbital. The s orbitals, though spherically symmetric, have radially placed wave-nodes for

6171: 6141: 6111: 5476: 5447: 3133: 2885: 2662: 2633: 1703:

determines the mean distance of the electron from the nucleus; all electrons with the same value of

13373: 13287: 12901: 12892: 12691: 12128:

Jeong, Jong Seok; Odlyzko, Michael L.; Xu, Peng; Jalan, Bharat; Mkhoyan, K. Andre (26 April 2016).

11142: 8586:

The shapes of atomic orbitals can be qualitatively understood by considering the analogous case of

8426: 7288:

themselves. The fifth and final d orbital consists of three regions of high probability density: a

7175:

fill space as symmetrically as possible, though with increasingly complex sets of lobes and nodes.

3770: 3730:{\displaystyle \psi _{n,\ell ,m}^{\text{real}}(r,\theta ,\phi )=R_{nl}(r)Y_{\ell m}(\theta ,\phi )} 2001: 1798: 1774: 1656: 1650: 1452: 1375: 1038: 970: 845: 9735:

screening from the charge of intervening electrons. Thus, in atoms with higher atomic number, the

6901:

which shows probability density but has no phase (which is lost when taking absolute value, since

396:

Electrons do not orbit a nucleus in the manner of a planet orbiting a star, but instead exist as

13363: 12910: 10888: 10803: 10749: 10707: 9600: 5803: 4327:{\textstyle \psi _{n,1,\pm 1}=R_{n,1}Y_{1}^{\pm 1}=\mp R_{n,1}{\sqrt {3/8\pi }}\cdot (x\pm iy)/r} 2190: 1970: 1662: 1631: 1075:(STO) is a form without radial nodes but decays from the nucleus as does a hydrogen-like orbital. 1004:

are quantum numbers). There are typically three mathematical forms for the radial functions

815:

This notation means that the corresponding Slater determinants have a clear higher weight in the

774: 199: 31: 11290: 11284: 10859:(symbol Fy). However, Feynman's approximation fails to predict the exact critical value of 6049: 5573: 3740: 1770:. The quantum numbers, together with the rules governing their possible values, are as follows: 1648:

A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers:

1379:

moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.

1276: 873: 726: 12846: 12668: 12450: 12444: 11642: 11182: 11147: 10211: 10200: 4135:

As an example of how the full orbital names are generated for real orbitals, one may calculate

3583: 2103: 2031: 1976: 706: 295: 146: 11578: 11340: 10820: 7322:, in fact it is possible to generate sets where all the d's are the same shape, just like the 13247: 13242: 12276: 11477: 10892: 10785: 10229:. Thus, two electrons may occupy a single orbital, so long as they have different values of 9708: 9682: 8591: 7318:. These shapes are not unique, and any linear combination is valid, like a transformation to 7181: 6426: 6207: 6080: 6016: 2474: 1935: 1909: 1876: 1347: 1337: 885: 750: 446: 437: 401: 61:. The two colors show the phase or sign of the wave function in each region. Each picture is 10817:, which accounts for relativistic effects, the wave function of the electron for atoms with 9402: 9364: 9326: 9094: 9056: 9018: 8758: 8720: 8682: 13213: 12617: 12417: 12372: 12310: 12248: 12213: 12178: 12141: 12082: 11863: 11797: 11750: 11489: 11447: 10310: 9801: 9738: 9662: 9642: 9554: 8621: 7239:

The shapes of p, d and f orbitals are described verbally here and shown graphically in the

7111: 4969: 4095: 3908: 3826: 2428: 2388: 2011: 1627: 1619: 1243: 833: 785: 681: 594: 298:

of atoms. They are derived from description by early spectroscopists of certain series of

243: 11921: 11717: 11547: 1363: 8: 13333: 13227: 12919: 11395: 11177: 11137: 9468: 8629: 8463: 7478: 7315: 7298:

Additionally, as is the case with the s orbitals, individual p, d, f and g orbitals with

4903: 2448: 1463: 1179: 1072: 974: 238: 98: 81:

function which depends on the coordinates of one electron. To see the elongated shape of

12621: 12421: 12376: 12314: 12252: 12217: 12182: 12145: 12086: 11867: 11801: 11754: 11493: 11451: 7295:

There are seven f orbitals, each with shapes more complex than those of the d orbitals.

3573:{\displaystyle \psi _{n,\ell ,m}(r,\theta ,\phi )=R_{nl}(r)Y_{\ell }^{m}(\theta ,\phi )} 1382:

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number

12771: 12734: 12706: 12549: 12483: 12345: 12326: 12264: 11879: 11766: 11505: 10844: 9781: 9758: 9622: 9574: 9534: 9514: 9494: 9448: 9442: 7212: 7036:, the orbital is vertical, counter rotating information is unknown, and the orbital is 5599: 4949: 4929: 4883: 4863: 4843: 4115: 4075: 3846: 3806: 2782: 2762: 2742: 2408: 2368: 1767: 1681: 1600: 1280: 1251: 1183: 1142: 1024: 877: 861: 758: 754: 661: 641: 574: 554: 530: 318: 12035: 11831:(2nd corrected ed.). New York, Berlin, Heidelberg: Springer-Verlag. p. 163. 11826: 9491:

orbital has the lowest possible energy in the atom. Each successively higher value of

7359: 13302: 13095: 13022: 12991: 12867: 12796: 12608:

Cohen, Irwin; Bustard, Thomas (1966). "Atomic Orbitals: Limitations and Variations".

12594: 12575: 12556: 12533: 12514: 12462: 12390: 12330: 12268: 12053: 12002: 11977: 11952: 11927: 11902: 11883: 11832: 11770: 11676: 11582: 11571: 11413: 11371: 11346: 11319: 11294: 11263: 11238: 11167: 11162: 10725: 10160: 7255: 7136: 6980: 1724: 1343: 1303: 1265: 1207: 1198:

turned out to have more in common with modern theory than any of its contemporaries.

1163: 1154: 881: 872:

Atomic orbitals can be the hydrogen-like "orbitals" which are exact solutions to the

722: 380: 106: 13036: 13007: 12970: 12804: 12740: 12625: 12454: 12425: 12380: 12318: 12256: 12221: 12186: 12149: 12090: 12031: 11871: 11805: 11758: 11709: 11651: 11615: 11539: 11509: 11497: 11455: 10688: 1781: 1707:

lie at the same average distance. For this reason, orbitals with the same value of

1272: 1247: 1079: 841: 457: 356: 344: 195: 116: 10173:

Atomic orbits are functions of three variables (two angles, and the distance

8616: orbitals, all of which have no angular momentum, might perhaps be that of a 7277:. The overall result is a lobe pointing along each direction of the primary axes. 7090:) have a single nodal plane between the lobes. The number of nodal spheres equals 13252: 12508: 11438: 11157: 10852: 8617: 3843:

have the same interpretation and significance as their complex counterparts, but

1790: 1591:, the letters associated with those numbers are K, L, M, N, O, ... respectively. 1239: 1216: 1195: 1190: 1158: 62: 10219:). These quantum numbers include the three that define orbitals, as well as the 7350: 7314:

The shapes of atomic orbitals in one-electron atom are related to 3-dimensional

6795: 1322:= 2 state can hold up to eight electrons in 2s and 2p subshells. In helium, all 856: 294:

respectively. These names, together with their n values, are used to describe

13195: 13179: 13174: 12884: 12857: 12800: 12790: 12154: 12129: 11202:

Orchin, Milton; Macomber, Roger S.; Pinhas, Allan; Wilson, R. Marshall (2005).

10814: 10303: 10287: 10204: 9436: 7319: 7267: 7259: 7157: 7051: 6984: 6918: 6856: 6822:. Only s orbitals invariably have a center anti-node; the other types never do. 3803:

common orbital visualizations. In real hydrogen-like orbitals, quantum numbers

2501: 2127:

available in that subshell. Empty cells represent subshells that do not exist.

1747: 1736: 1712: 1670: 1581: 1580:

There is also another, less common system still used in X-ray science known as

1575: 1307: 1032: 797: 781: 762: 734: 730: 461: 452:

One should remember that these orbital 'states', as described here, are merely

348: 314: 177: 166: 162: 11713: 11655: 11619: 11543: 10354:

The "periodic" nature of the filling of orbitals, as well as emergence of the

7083:) are spherically symmetric and have no nodal planes, whereas the p orbitals ( 1178:'s discovery of the electron in 1897, it became clear that atoms were not the 30:"Orbital shell" redirects here. For the collection of spaceflight orbits, see 13357: 13268: 13208: 13203: 13184: 13078: 13012: 12986: 11971: 11390: 10912: 10683: 10168: 7398: 7076:

radial nodal planes passing through the origin. For example, the s orbitals (

6977: 6860: 4009:

orbitals. With this one can already assign names to complex orbitals such as

1677: 1635: 1606: 1367: 1175: 1136: 793: 635: 412: 397: 336: 302: 12648: 7156:

its orientation. However, since some orbitals are described by equations in

1219:. This constraint automatically allowed only certain electron energies. The 777:, for example, depends on the correlations of the motion of the electrons.) 237:

An orbital can be occupied by a maximum of two electrons, each with its own

12720: 12654: 12651:, a visualization of all common and uncommon atomic orbitals, from 1s to 7g 12446:

Superheavy elements: a prediction of their chemical and physical properties

12394: 12385: 12360: 11152: 10848: 10682:

The number of electrons in an electrically neutral atom increases with the

9616: 8612:

A mental "planetary orbit" picture closest to the behavior of electrons in

8446: 2688:

orbitals. This animation does not use the Condon–Shortley phase convention.

1260: 306: 299: 13047: 11976:. Translated by from the French by Susan Reid Hemley. Wiley-Interscience. 11951:(Two vol. bound as one, unabridged reprint ed.). Mineola, NY: Dover. 11459: 10349:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

10309:

The periodic table may also be divided into several numbered rectangular '

9603:

effects. The latter induce tiny binding energy differences especially for

2626: 1338:

Modern conceptions and connections to the Heisenberg uncertainty principle

1310:

and subshells which can each hold a number of electrons determined by the

1286:

The Bohr model was able to explain the emission and absorption spectra of

13169: 13164: 13159: 12815: 11922:

Petrucci, Ralph; Herring, F.; Madura, Jeffry; Bissonnette, Carey (2016).

11852:

Gerlach, W.; Stern, O. (1922). "Das magnetische Moment des Silberatoms".

8486:

orbitals where are eigenstates of the orbital angular momentum operator,

8454: 8450: 2618:—where an atom is exposed to a magnetic field—provides one such example. 1743: 1615: 1355: 801: 453: 400:. Thus the lowest possible energy an electron can take is similar to the 366: 170: 150: 10911:

of the period due to properties similar to p subshells in ordinary

9775:

of electrons becomes less and less important in their energy placement.

8460:

These are the real-valued orbitals commonly used in chemistry. Only the

7129:

increases, the size of the orbital increases. The higher nuclear charge

13151: 13135: 13125: 13031: 12747: 12458: 12322: 12296: 12260: 11972:

Claude Cohen-Tannoudji; Bernard Diu; Franck Laloë; et al. (1996).

11875: 11762: 10856: 10736: 10677:

Electron configuration § Atoms: Aufbau principle and Madelung rule

10299: 9608: 8442: 8430: 7311:

further increase the number of radial nodes, for each type of orbital.

6828: 4092:

quantum number, the second character is the symbol for that particular

1696: 1623: 1351: 1231: 1220: 1212: 1150: 738: 548: 12629: 12429: 12225: 12094: 12021: 11368:

The Feynman Lectures on Physics – The Definitive Edition, Vol 1 lect 6

11342:

Quanta, Matter, and Change: A Molecular Approach to Physical Chemistry

6997:

modes; the projection of the orbital onto the xy plane has a resonant

2567:. These values are also called "spin up" or "spin down" respectively. 709:

of eigenstates by superimposing eigenstates from any other basis (see

13273: 12190: 11810: 11785: 11501: 10338: 10330: 8083: 8076: 7401:

phases shown in two different colors (arbitrarily red and blue). The

7251: 1403:

Orbitals have been given names, which are usually given in the form:

737:. Specifically, in quantum mechanics, the state of an atom, i.e., an 405: 176:

Each orbital in an atom is characterized by a set of values of three

12408:

Szabo, Attila (1969). "Contour diagrams for relativistic orbitals".

12299:(1923). "Über die Anwendung der Quantumtheorie auf den Atombau. I". 11603: 10950:

corresponding with the exact energy difference between said states.

10155: 8069: 1758: 428:

Electrons jump between orbitals like particles. For example, if one

13140: 11786:"The Quantum Postulate and the Recent Development of Atomic Theory" 8648:

and the wave functions for a vibrating sphere are three-coordinate

8625: 8602: 7263: 1374:

suggested that the electron's position needed to be described by a

1371: 1287: 1157:, that of the electron moving around a nucleus. Japanese physicist 432:

strikes the electrons, only one electron changes state as a result.

363:= 4s3d and Cr = 3d) can be rationalized only somewhat arbitrarily. 360: 154: 7125:

determines size and energy of the orbital for a given nucleus; as

1226: 425:

The number of electrons orbiting a nucleus can be only an integer.

198:, and its orbital angular momentum projected along a chosen axis ( 13130: 10908: 10729: 10326: 8419:

No elements with 6f, 7d or 7f electrons have been discovered yet.

7947: 3619:

the radial part of the orbital, this definition is equivalent to

1958:. The set of orbitals associated with a particular value of 824: 12660: 10294:, it consists of elements whose outermost electrons fall in the 3863:

is no longer a good quantum number (but its absolute value is).

1186:" was the most widely accepted explanation of atomic structure. 173:

of finding an electron in a specific region around the nucleus.

39: 10928: 10334: 10280: 8624:

of 1 but a finite major axis, not physically possible (because

8062: 8055: 8048: 7387: 6941:

orbital graphs tend to have less spherical, thinner lobes than

5502:

orbitals may appear, for example, as the sum and difference of

2596:

The above conventions imply a preferred axis (for example, the

1326: = 1 states are fully occupied; the same is true for 1295: 429: 11366:

Feynman, Richard; Leighton, Robert B.; Sands, Matthew (2006).

9599:), and by the effect of the magnetic field of the nucleus and 7940: 7933: 7926: 3866:

Some real orbitals are given specific names beyond the simple

1686:

Linear combination of atomic orbitals molecular orbital method

1318: = 1 state can hold one or two electrons, while the 844:

approximation, which is one way to reduce the complexities of

12169:

Powell, Richard E. (1968). "The five equivalent d orbitals".

10932: 10209:

Several rules govern the placement of electrons in orbitals (

8632:

of orbits with equal major axes but increasing eccentricity.

7850: 7843: 7289: 7215:(densest at center and fades outward exponentially), but for 6878:

is often indicated in each subregion of the orbital picture.

2630:

Animation of continuously varying superpositions between the

1299: 10150: 4926:

polynomial except for the term with the highest exponent in

4677:{\textstyle \psi _{n,1,0}=R_{n,1}{\sqrt {3/4\pi }}\cdot z/r} 2586:), these two electrons must differ in their spin projection 122: 43:

The shapes of the first five atomic orbitals are: 1s, 2s, 2p

12114:. North-Holland Publishing Company - Amsterdam. p. 39. 12050:

General chemistry : principles and modern applications

8425:

Elements with 7p electrons have been discovered, but their

3449: 3121: 1821:

ranges across all (integer) values satisfying the relation

1723:

are even more closely related, and are said to comprise a "

805: 404:

of a wave on a string. Higher energy states are similar to

359:

in which they are said to be populated by electrons (e.g.,

194:, which respectively correspond to electron's energy, its 158: 134: 11201: 10333:

respectively belong to the 2s subshell, and those of

8156: 8034: 1302:(18 electrons) exhibit similar chemical inertness. Modern 634:; it is ambiguous, either 0.0 or 1.0. A superposition of 618:

is a superposition of 0 and 1. It is not a fraction like

387:. In this sense, electrons have the following properties: 11339:

Atkins, Peter; de Paula, Julio; Friedman, Ronald (2009).

10903:

is expected to exist, where "3/2" and "1/2" refer to the

6983:

patterns between the two counter-rotating, ring-resonant

1610: 551:. So, for the three states just mentioned, the value of 128: 8020: 2524:. Its projection along a specified axis is given by the 721:

Atomic orbitals may be defined more precisely in formal

11521: 11519: 11237:. New York: Oxford University Press. pp. 407–409. 8318: 8215: 8208: 8149: 8142: 8135: 8128: 8107: 8100: 8041: 8027: 8013: 8006: 7985: 7978: 7919: 7898: 7891: 7836: 7829: 7782: 4900:

appearing in the numerator. We ignore any terms in the

2500:

Each electron also has angular momentum in the form of

864:

atomic orbitals showing probability density and phase (

716: 283:

refer to orbitals with angular momentum quantum number

11338: 11064:

By quantum theory, state 1 has a fixed energy of

10286:

This behavior is responsible for the structure of the

8581: 8229: 8222: 8121: 8114: 7999: 7992: 7912: 7905: 7167:

also. Together, the whole set of orbitals for a given

4600: 4192: 1762:

Energetic levels and sublevels of polyelectronic atoms

12359:

Poliakoff, Martyn; Tang, Samantha (9 February 2015).

11924:

General chemistry: principles and modern applications

10823: 10788: 10752: 9804: 9784: 9761: 9741: 9711: 9685: 9665: 9645: 9625: 9577: 9557: 9537: 9517: 9511:

has a higher energy, but the difference decreases as

9497: 9471: 9451: 9405: 9367: 9329: 9261: 9198: 9135: 9097: 9059: 9021: 8925: 8862: 8799: 8761: 8723: 8685: 8577:

Atomic orbitals spdf m-eigenstates and superpositions

8528: 8492: 8466: 7184: 6730: 6671: 6631: 6594: 6554: 6518: 6456: 6429: 6375: 6342: 6305: 6272: 6239: 6210: 6174: 6144: 6114: 6083: 6052: 6019: 5958: 5899: 5840: 5806: 5747: 5688: 5629: 5602: 5596:

so there does not seem be consensus on the naming of

5576: 5540: 5508: 5479: 5450: 4995: 4972: 4952: 4932: 4906: 4886: 4866: 4846: 4693: 4406: 4340: 4141: 4118: 4098: 4078: 4065:{\displaystyle 2{\text{p}}_{\pm 1}=\psi _{2,1,\pm 1}} 4015: 3990: 3931: 3911: 3872: 3849: 3829: 3809: 3773: 3743: 3625: 3586: 3471: 2849: 2805: 2785: 2765: 2745: 2706: 2665: 2636: 2477: 2451: 2431: 2411: 2391: 2371: 2193: 2106: 2061: 2034: 2014: 1979: 1938: 1912: 1879: 1827: 1780:

describes the energy of the electron and is always a

1518: 1412: 1088: 1041: 684: 664: 644: 597: 577: 557: 533: 246: 12238: 11516: 11365: 7262:(the two-lobed shape is sometimes referred to as a " 6885:

function is graphed to show its phases, rather than

1027:. The part of the function that depends on distance 773:

of products of single electron wave functions. (The

137: 131: 125: 12945:

Electron configurations of the elements (data page)

12532:(4 ed.). New York: W. H. Freeman and Company. 12127: 12001:(7th ed.). Pearson Education. pp. 141–2. 5616:orbitals or higher according to this nomenclature. 4002:{\displaystyle {\text{s, p, d, f, g, h, i}}\ldots } 547:(2, 1, 1). For each eigenstate, a property has an 119: 12551:The Periodic Table, Its Story and Its Significance 12548: 12513:. Singapore: World Scientific Publishing Company. 11570: 10835: 10794: 10770: 10275:), at most two electrons can occupy each orbital. 9810: 9790: 9767: 9747: 9723: 9697: 9671: 9651: 9631: 9583: 9563: 9543: 9523: 9503: 9483: 9457: 9418: 9380: 9342: 9298: 9235: 9172: 9110: 9072: 9034: 8962: 8899: 8836: 8774: 8736: 8698: 8558: 8514: 8478: 7196: 6777: 6715: 6656: 6616: 6579: 6539: 6503: 6441: 6410: 6360: 6327: 6290: 6257: 6222: 6189: 6159: 6129: 6095: 6060: 6031: 6002: 5943: 5884: 5825: 5791: 5732: 5673: 5608: 5588: 5558: 5526: 5494: 5465: 5429: 4978: 4958: 4938: 4918: 4892: 4872: 4852: 4829: 4676: 4583: 4389: 4326: 4174: 4124: 4104: 4084: 4064: 4001: 3976: 3917: 3897: 3855: 3835: 3815: 3791: 3759: 3729: 3611: 3572: 3455: 2835: 2791: 2771: 2751: 2731: 2680: 2651: 2489: 2463: 2437: 2417: 2397: 2377: 2212: 2119: 2089: 2047: 2020: 1992: 1950: 1924: 1891: 1858: 1549: 1436: 1114: 1060: 697: 670: 650: 610: 583: 563: 539: 259: 216:orbitals, and are often labeled using associated 12365:Philosophical Transactions of the Royal Society A 12073:Friedman (1964). "The shapes of the f orbitals". 11949:Quantum mechanics : two volumes bound as one 10882: 10847:. The significance of element 137, also known as 10721:6s valence electrons becoming lowered in energy. 7449:orbitals (which is why they are listed under the 1398: 796:of an atom. These states are labeled by a set of 13355: 12449:. Structure and Bonding. Vol. 21. pp. 11471: 11469: 11211:The Vocabulary and Concepts of Organic Chemistry 9255:Wave function of 4p orbital (real part, 2D-cut, 9192:Wave function of 3p orbital (real part, 2D-cut, 9129:Wave function of 2p orbital (real part, 2D-cut, 8919:Wave function of 3s orbital (real part, 2D-cut, 8856:Wave function of 2s orbital (real part, 2D-cut, 8793:Wave function of 1s orbital (real part, 2D-cut, 7435:are formed by taking linear combinations of the 725:language. They are approximate solutions to the 638:(2, 1, 1) and (3, 2, 1) would have an ambiguous 101:more directly, see pictures of d-orbitals below. 12527: 12204:Kimball, George E. (1940). "Directed Valence". 12123: 12121: 10938: 10195:Atomic orbitals and periodic table construction 4175:{\displaystyle \psi _{n,1,\pm 1}^{\text{real}}} 2836:{\displaystyle \psi _{n,\ell ,m}^{\text{real}}} 1788:; these orbitals together are sometimes called 331:Atomic orbitals are basic building blocks of 12107: 10907:. This "pp" hybrid may be responsible for the 2739:denote a complex orbital with quantum numbers 2090:{\displaystyle -\ell \leq m_{\ell }\leq \ell } 1750:versions of the atomic orbitals are employed. 1082:(Gaussians) has no radial nodes and decays as 13063: 12831: 12676: 12510:Orbitals: With Applications in Atomic Spectra 12358: 11466: 11313: 10855:. Element 137 is sometimes informally called 4390:{\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}} 1462:is a lower-case letter denoting the shape or 12607: 12281:: CS1 maint: multiple names: authors list ( 12118: 11851: 11478:"On the Constitution of Atoms and Molecules" 11412:(4th ed.). Prentice-Hall. p. 262. 7354:The 1s, 2s, and 2p orbitals of a sodium atom 6859:is everywhere non-negative, the sign of the 6778:{\displaystyle {\text{f}}_{x(x^{2}-3y^{2})}} 6504:{\displaystyle {\text{f}}_{y(3x^{2}-y^{2})}} 13077: 11370:. Pearson PLC, Addison Wesley. p. 11. 11314:Laidler, Keith J.; Meiser, John H. (1982). 10686:. The electrons in the outermost shell, or 8628:were to collide), but can be imagined as a 7390:and some beyond. "ψ" graphs are shown with 7068:. An orbital with azimuthal quantum number 6716:{\displaystyle {\text{f}}_{z(x^{2}-y^{2})}} 2425:is represented by its numerical value, but 729:for the electrons bound to the atom by the 13070: 13056: 12845: 12838: 12824: 12683: 12669: 12361:"The periodic table: icon and inspiration" 11738: 11595: 10953:Consider two states of the hydrogen atom: 9299:{\displaystyle r_{\mathrm {max} }=25a_{0}} 9236:{\displaystyle r_{\mathrm {max} }=20a_{0}} 9173:{\displaystyle r_{\mathrm {max} }=10a_{0}} 8963:{\displaystyle r_{\mathrm {max} }=20a_{0}} 8900:{\displaystyle r_{\mathrm {max} }=10a_{0}} 8429:are only predicted – save the exceptional 3905:designation. Orbitals with quantum number 2365:Subshells are usually identified by their 1298:(two electrons), neon (10 electrons), and 234:) which describe their angular structure. 27:Function describing an electron in an atom 12588: 12384: 12153: 12111:The Wave Mechanics Of Electrons In Metals 11990: 11809: 11257: 11073:, and state 2 has a fixed energy of 10851:, was first pointed out by the physicist 10302:was the first to propose (1923) that the 10151:Electron placement and the periodic table 8983:In addition, the drum modes analogous to 8837:{\displaystyle r_{\mathrm {max} }=2a_{0}} 8566:are combinations of two eigenstates. See 6003:{\displaystyle \psi _{m=-3}-\psi _{m=+3}} 5944:{\displaystyle \psi _{m=-2}-\psi _{m=+2}} 5885:{\displaystyle \psi _{m=-1}-\psi _{m=+1}} 5792:{\displaystyle \psi _{m=-1}+\psi _{m=+1}} 5733:{\displaystyle \psi _{m=-2}+\psi _{m=+2}} 5674:{\displaystyle \psi _{m=-3}+\psi _{m=+3}} 1594: 1522: 1451:is the energy level corresponding to the 1416: 957:. The angular factors of atomic orbitals 12940:Periodic table (electron configurations) 12644:3D representation of hydrogenic orbitals 12072: 12024:Journal of Molecular Structure: THEOCHEM 11675:. Simon & Schuster. pp. 50–51. 11435: 11345:. Oxford University Press. p. 106. 11230: 10181: 10167:) is arranged by increasing energy (see 10154: 8572: 7349: 7135: 6799:Transparent cloud view of a computed 6s 6794: 6411:{\displaystyle {\text{d}}_{x^{2}-y^{2}}} 4112:quantum number and the subscript is the 2625: 2055:obtains the integer values in the range 1757: 1550:{\displaystyle X\,\mathrm {type} ^{y}\ } 1498:are denoted as p, d and f respectively. 1354:noted that the existence of any sort of 1225: 855: 365: 161:. This function describes an electron's 38: 12528:Tipler, Paul; Llewellyn, Ralph (2003). 12436: 12203: 11946: 11896: 11824: 11695: 11632: 11601: 11525: 10746: electron has a velocity given by 10695: 1859:{\displaystyle 0\leq \ell \leq n_{0}-1} 1484:) and has an angular quantum number of 745:, is approximated by an expansion (see 14: 13356: 12569: 12546: 12442: 12346:"Primer on Quantum Theory of the Atom" 12241:Communications in Mathematical Physics 12168: 11996: 11668: 11568: 11407: 11289:(5 ed.). Prentice Hall. pp. 11282: 7005:there are two standing wave solutions 1501:The set of orbitals for a given n and 374: 13051: 12819: 12664: 12555:. New York: Oxford University Press. 12506: 12407: 11828:Quantum mechanics : Introduction 10905:total angular momentum quantum number 10712:For elements with high atomic number 8559:{\displaystyle m=\pm 1,\pm 2,\cdots } 6790: 1466:of the orbital, corresponding to the 12295: 12289: 11783: 11573:A Short History of Nearly Everything 11475: 11220:from the original on 9 October 2022. 9004:p-type drum modes and wave functions 8668:s-type drum modes and wave functions 3977:{\displaystyle 0,1,2,3,4,5,6\ldots } 1962:are sometimes collectively called a 1437:{\displaystyle X\,\mathrm {type} \ } 1386:for each orbital became known as an 969:generate s, p, d, etc. functions as 717:Formal quantum mechanical definition 12574:(7th ed.). Pearson Education. 11262:. Prentice Hall. pp. 190–191. 11173:Quantum chemistry computer programs 11133:Atomic electron configuration table 8582:Qualitative understanding of shapes 8568:comparison in the following picture 7149:determines an orbital's shape, and 6657:{\displaystyle {\text{f}}_{xz^{2}}} 6580:{\displaystyle {\text{f}}_{yz^{2}}} 5566:, contrary to what is shown above. 1906: shell has only orbitals with 1873: shell has only orbitals with 1753: 1715:". Orbitals with the same value of 1290:. The energies of electrons in the 1189:Shortly after Thomson's discovery, 851: 496:(2, 1, 1), or even the mixed state 169:, and can be used to calculate the 24: 11926:(11th ed.). : Prentice Hall. 11318:. Benjamin/Cummings. p. 488. 9274: 9271: 9268: 9211: 9208: 9205: 9148: 9145: 9142: 8938: 8935: 8932: 8875: 8872: 8869: 8812: 8809: 8806: 7094:, consistent with the restriction 6617:{\displaystyle {\text{f}}_{z^{3}}} 6328:{\displaystyle {\text{d}}_{z^{2}}} 1730: 1534: 1531: 1528: 1525: 1427: 1424: 1421: 1418: 1180:smallest building blocks of nature 1147:one-electron orbital wave function 710: 25: 13390: 13101:Introduction to quantum mechanics 12873:Introduction to quantum mechanics 12690: 12637: 12593:(2 ed.). Benjamin Cummings. 12591:Introduction to Quantum Mechanics 12343: 11899:Advanced visual quantum mechanics 11260:Introduction to Quantum Mechanics 10163:orbitals. The chart of orbitals ( 9430: 8588:standing waves on a circular drum 7381: 7374:) is spherical. This is known as 7160:, the shape sometimes depends on 5440:The expression above all use the 4684:. As a more complicated example: 3898:{\displaystyle \psi _{n,\ell ,m}} 2732:{\displaystyle \psi _{n,\ell ,m}} 1569: 1141:The term "orbital" was coined by 1115:{\displaystyle e^{-\alpha r^{2}}} 12795: 12786: 12785: 9392: 9354: 9316: 9248: 9185: 9122: 9084: 9046: 9008: 8912: 8849: 8786: 8748: 8710: 8672: 8592:Heisenberg uncertainty principle 8317: 8228: 8221: 8214: 8207: 8155: 8148: 8141: 8134: 8127: 8120: 8113: 8106: 8099: 8082: 8075: 8068: 8061: 8054: 8047: 8040: 8033: 8026: 8019: 8012: 8005: 7998: 7991: 7984: 7977: 7946: 7939: 7932: 7925: 7918: 7911: 7904: 7897: 7890: 7849: 7842: 7835: 7828: 7781: 7280:Four of the five d orbitals for 7243:below. The three p orbitals for 6540:{\displaystyle {\text{f}}_{xyz}} 5442:Condon–Shortley phase convention 2698:Condon–Shortley phase convention 2621: 1719:and also the same value of 1393: 884:chosen for orbitals are usually 115: 12401: 12352: 12337: 12232: 12206:The Journal of Chemical Physics 12197: 12162: 12101: 12066: 12042: 12015: 11965: 11940: 11915: 11890: 11845: 11818: 11777: 11732: 11689: 11662: 11626: 11562: 11429: 10923:come close due to relativistic 9619:of orbitals depend not only on 8594:for details of the mechanism). 8433:, which fills 7p instead of 6d. 7204:) are shaped like spheres. For 6361:{\displaystyle {\text{d}}_{xz}} 6291:{\displaystyle {\text{d}}_{yz}} 6258:{\displaystyle {\text{d}}_{xy}} 5559:{\displaystyle {\text{p}}_{-1}} 5527:{\displaystyle {\text{p}}_{+1}} 1609:. An atom of any other element 1468:angular momentum quantum number 1169: 339:atomic orbitals. The repeating 11401: 11384: 11359: 11332: 11307: 11276: 11251: 11234:Oxford Dictionary of Chemistry 11224: 11195: 10883:pp hybridization (conjectured) 10702:Relativistic quantum chemistry 10243:takes one of only two values ( 8515:{\displaystyle {\hat {L}}_{z}} 8500: 7470:are not the same shape as the 6831:where the probability density 6770: 6741: 6708: 6682: 6496: 6467: 6190:{\displaystyle {\text{p}}_{x}} 6160:{\displaystyle {\text{p}}_{z}} 6130:{\displaystyle {\text{p}}_{y}} 5495:{\displaystyle {\text{p}}_{y}} 5466:{\displaystyle {\text{p}}_{x}} 4811: 4782: 4313: 4298: 3724: 3712: 3696: 3690: 3671: 3653: 3606: 3600: 3567: 3555: 3537: 3531: 3512: 3494: 3419: 3411: 3384: 3374: 3365: 3357: 3293: 3285: 3236: 3228: 3201: 3191: 3182: 3174: 3092: 3084: 3048: 3038: 3005: 2997: 2949: 2941: 2905: 2895: 2681:{\displaystyle {\text{p}}_{x}} 2652:{\displaystyle {\text{p}}_{1}} 2333:−4, −3, −2, −1, 0, 1, 2, 3, 4 2002:magnetic moment of an electron 1491:, denoted as s. Orbitals with 1399:Orbital notation and subshells 868:orbitals and higher not shown) 757:of anti-symmetrized products ( 408:of that fundamental frequency. 343:of blocks of 2, 6, 10, and 14 13: 1: 12657:Still images of many orbitals 12410:Journal of Chemical Education 12171:Journal of Chemical Education 12036:10.1016/S0166-1280(97)00185-1 11696:Nagaoka, Hantaro (May 1904). 11672:The Making of the Atomic Bomb 11526:Nagaoka, Hantaro (May 1904). 11189: 3792:{\displaystyle Y_{\ell }^{m}} 1061:{\displaystyle e^{-\alpha r}} 12774:(relativistic quantum model) 11901:. New York: Springer/TELOS. 10939:Transitions between orbitals 10221:spin magnetic quantum number 9441:In atoms with one electron ( 4184:table of spherical harmonics 2526:spin magnetic quantum number 1684:) of multiple orbitals. See 1201: 1031:from the nucleus has radial 149:describing the location and 7: 12933:Ground-state configurations 11577:. Broadway Books. pp. 11125: 10771:{\displaystyle v=Z\alpha c} 9595:and another quantum number 7410:orbital is the same as the 5826:{\displaystyle \psi _{m=0}} 2213:{\displaystyle m_{\ell }=0} 788:correspond to transitions ( 32:Orbital shell (spaceflight) 10: 13395: 12902:Azimuthal quantum number ( 12893:Principal quantum number ( 12507:McCaw, Charles S. (2015). 12155:10.1103/PhysRevB.93.165140 11784:Bohr, Niels (April 1928). 11204:"1. Atomic Orbital Theory" 10945:Atomic electron transition 10942: 10705: 10699: 10198: 9434: 6061:{\displaystyle {\text{s}}} 5589:{\displaystyle \ell >3} 4072:; the first symbol is the 3760:{\displaystyle Y_{\ell m}} 1734: 1598: 1573: 1306:explains this in terms of 1134: 1130: 771:independent-particle model 29: 13321: 13295: 13286: 13261: 13235: 13226: 13193: 13149: 13118: 13111: 13086: 13021: 13000: 12979: 12961:Pauli exclusion principle 12953: 12932: 12911:Magnetic quantum number ( 12883: 12853: 12781: 12757: 12714:vortex theory of the atom 12698: 12589:Griffiths, David (2000). 12443:Fricke, Burkhard (1975). 12052:. : Prentice Hall. 2016. 11714:10.1080/14786440409463141 11656:10.1080/14786440409463107 11620:10.1080/14786449708621070 11544:10.1080/14786440409463141 11258:Griffiths, David (1995). 10341:to the 3s subshell. 10217:Pauli exclusion principle 8427:electronic configurations 7604: 7596: 7588: 7572: 7564: 7548: 7518: 7508: 7498: 6976:The lobes can be seen as 3612:{\displaystyle R_{nl}(r)} 2572:Pauli exclusion principle 2120:{\displaystyle m_{\ell }} 2048:{\displaystyle m_{\ell }} 2008:model. Within a subshell 1993:{\displaystyle m_{\ell }} 1312:Pauli exclusion principle 829:Pauli exclusion principle 817:configuration interaction 765:component, one speaks of 747:configuration interaction 591:is 1. But the value for 420:Particle-like properties: 13288:Molecular orbital theory 11947:Messiah, Albert (1999). 11825:Greiner, Walter (1994). 11742:Zeitschrift für Physik A 11669:Rhodes, Richard (1995). 11143:Condensed matter physics 10836:{\displaystyle Z>137} 2616:Stern–Gerlach experiment 1799:azimuthal quantum number 1775:principal quantum number 1711:are said to comprise a " 1453:principal quantum number 1376:probability distribution 846:molecular orbital theory 379:With the development of 196:orbital angular momentum 12108:Stanley Raimes (1963). 11897:Thaller, Bernd (2004). 11633:Thomson, J. J. (1904). 11602:Thomson, J. J. (1897). 11408:Levine, Ira N. (1991). 11213:(2nd ed.). Wiley. 10804:fine-structure constant 10795:{\displaystyle \alpha } 10708:Extended periodic table 10279:energy (by releasing a 9724:{\displaystyle \ell =3} 9698:{\displaystyle \ell =2} 9601:quantum electrodynamics 7197:{\displaystyle \ell =0} 7178:The single s orbitals ( 7145:Also in general terms, 6442:{\displaystyle \ell =3} 6223:{\displaystyle \ell =2} 6096:{\displaystyle \ell =1} 6032:{\displaystyle \ell =0} 2502:quantum mechanical spin 2490:{\displaystyle \ell =0} 2303:−3, −2, −1, 0, 1, 2, 3 1971:magnetic quantum number 1951:{\displaystyle \ell =1} 1925:{\displaystyle \ell =0} 1892:{\displaystyle \ell =0} 1676:The stationary states ( 1632:trigonometric functions 775:London dispersion force 571:is 2, and the value of 296:electron configurations 200:magnetic quantum number 12847:Electron configuration 12386:10.1098/rsta.2014.0211 12302:Zeitschrift für Physik 11855:Zeitschrift für Physik 11702:Philosophical Magazine 11643:Philosophical Magazine 11608:Philosophical Magazine 11532:Philosophical Magazine 11482:Philosophical Magazine 11183:Wave function collapse 11148:Electron configuration 10837: 10796: 10782:is the atomic number, 10772: 10212:electron configuration 10201:Electron configuration 10196: 10179: 9812: 9792: 9769: 9749: 9725: 9699: 9673: 9653: 9633: 9585: 9565: 9545: 9525: 9505: 9485: 9459: 9420: 9419:{\displaystyle u_{23}} 9382: 9381:{\displaystyle u_{22}} 9344: 9343:{\displaystyle u_{21}} 9300: 9237: 9174: 9112: 9111:{\displaystyle u_{13}} 9074: 9073:{\displaystyle u_{12}} 9036: 9035:{\displaystyle u_{11}} 8964: 8901: 8838: 8776: 8775:{\displaystyle u_{03}} 8738: 8737:{\displaystyle u_{02}} 8700: 8699:{\displaystyle u_{01}} 8578: 8560: 8516: 8480: 7477:, since they are pure 7355: 7198: 7142: 6823: 6779: 6717: 6658: 6618: 6581: 6541: 6505: 6443: 6412: 6362: 6329: 6292: 6259: 6224: 6191: 6161: 6131: 6097: 6062: 6033: 6004: 5945: 5886: 5827: 5793: 5734: 5675: 5610: 5590: 5560: 5528: 5496: 5467: 5431: 4980: 4960: 4940: 4920: 4894: 4874: 4854: 4831: 4678: 4585: 4391: 4328: 4176: 4126: 4106: 4086: 4066: 4003: 3978: 3919: 3899: 3857: 3837: 3817: 3793: 3761: 3731: 3613: 3574: 3457: 2837: 2793: 2773: 2753: 2733: 2689: 2682: 2653: 2491: 2465: 2439: 2419: 2399: 2379: 2330:−3, −2, −1, 0, 1, 2, 3 2214: 2121: 2091: 2049: 2022: 1994: 1952: 1926: 1893: 1860: 1763: 1695:first appeared in the 1595:Hydrogen-like orbitals 1551: 1438: 1242:'s explanation of the 1235: 1116: 1062: 1021:hydrogen-like orbitals 869: 699: 672: 652: 612: 585: 565: 541: 371: 261: 102: 13001:Bonding participation 12920:Spin quantum number ( 12709:(billiard ball model) 12547:Scerri, Eric (2007). 11569:Bryson, Bill (2003). 11460:10.1103/PhysRev.41.49 11231:Daintith, J. (2004). 10915:. Energy levels of 8p 10838: 10797: 10773: 10321:associated with that 10194: 10158: 9813: 9811:{\displaystyle \ell } 9793: 9770: 9750: 9748:{\displaystyle \ell } 9726: 9700: 9674: 9672:{\displaystyle \ell } 9654: 9652:{\displaystyle \ell } 9634: 9586: 9566: 9564:{\displaystyle \ell } 9546: 9526: 9506: 9486: 9460: 9421: 9383: 9345: 9301: 9238: 9175: 9113: 9075: 9037: 8965: 8902: 8839: 8777: 8739: 8701: 8576: 8561: 8517: 8481: 7353: 7250:have the form of two 7199: 7139: 6798: 6780: 6718: 6659: 6619: 6582: 6542: 6506: 6444: 6413: 6363: 6330: 6293: 6260: 6225: 6192: 6162: 6132: 6098: 6063: 6034: 6005: 5946: 5887: 5828: 5794: 5735: 5676: 5611: 5591: 5561: 5529: 5497: 5468: 5432: 4981: 4979:{\displaystyle \ell } 4961: 4941: 4921: 4895: 4875: 4855: 4832: 4679: 4586: 4392: 4329: 4177: 4127: 4107: 4105:{\displaystyle \ell } 4087: 4067: 4004: 3979: 3920: 3918:{\displaystyle \ell } 3900: 3858: 3838: 3836:{\displaystyle \ell } 3818: 3794: 3762: 3732: 3614: 3575: 3458: 2838: 2794: 2774: 2754: 2734: 2683: 2654: 2629: 2492: 2466: 2440: 2438:{\displaystyle \ell } 2420: 2400: 2398:{\displaystyle \ell } 2380: 2215: 2122: 2092: 2050: 2023: 2021:{\displaystyle \ell } 1995: 1953: 1927: 1894: 1861: 1761: 1552: 1439: 1348:uncertainty principle 1232:Rutherford–Bohr model 1229: 1145:in 1932 as short for 1117: 1080:Gaussian type orbital 1063: 886:spherical coordinates 859: 786:atomic spectral lines 700: 698:{\displaystyle m_{l}} 673: 653: 613: 611:{\displaystyle m_{l}} 586: 566: 542: 447:uncertainty principle 402:fundamental frequency 391:Wave-like properties: 385:wave–particle duality 369: 262: 260:{\displaystyle m_{s}} 42: 12766:electron cloud model 12723:(cubical atom model) 12570:Levine, Ira (2014). 11997:Levine, Ira (2014). 11476:Bohr, Niels (1913). 11283:Levine, Ira (2000). 10821: 10786: 10750: 10696:Relativistic effects 10159:Electron atomic and 9802: 9782: 9759: 9739: 9709: 9683: 9663: 9643: 9623: 9575: 9555: 9535: 9531:increases. For high 9515: 9495: 9469: 9449: 9403: 9365: 9327: 9259: 9196: 9133: 9095: 9057: 9019: 8923: 8860: 8797: 8759: 8721: 8683: 8622:orbital eccentricity 8526: 8490: 8464: 8457:are still missing). 7347:are the same shape. 7182: 7102:. Loosely speaking, 7040:-axis symmetric. If 6855:as the square of an 6728: 6669: 6629: 6592: 6552: 6516: 6454: 6427: 6373: 6340: 6303: 6270: 6237: 6208: 6172: 6142: 6112: 6081: 6050: 6017: 5956: 5897: 5838: 5804: 5745: 5686: 5627: 5600: 5574: 5538: 5506: 5477: 5448: 4993: 4970: 4950: 4930: 4904: 4884: 4864: 4844: 4691: 4598: 4404: 4338: 4190: 4139: 4116: 4096: 4076: 4013: 3988: 3929: 3909: 3870: 3847: 3827: 3807: 3771: 3741: 3623: 3584: 3469: 2847: 2803: 2799:, the real orbitals 2783: 2763: 2743: 2704: 2663: 2634: 2497:as a '2s subshell'. 2475: 2449: 2429: 2409: 2389: 2369: 2191: 2104: 2059: 2032: 2012: 1977: 1936: 1910: 1877: 1866:. For instance, the 1825: 1620:Hamiltonian operator 1589:= 1, 2, 3, 4, 5, ... 1516: 1410: 1277:Schrödinger equation 1244:photoelectric effect 1238:After Bohr's use of 1234:of the hydrogen atom 1086: 1039: 878:hydrogen-like "atom" 874:Schrödinger equation 834:electron correlation 767:atomic spin orbitals 727:Schrödinger equation 682: 662: 642: 595: 575: 555: 531: 347:within sections of 333:atomic orbital model 244: 218:harmonic polynomials 97:functions that show 13228:Valence bond theory 12750:(old quantum model) 12622:1966JChEd..43..187C 12422:1969JChEd..46..678S 12377:2015RSPTA.37340211P 12315:1923ZPhy...13..117B 12253:1982CMaPh..85..549C 12218:1940JChPh...8..188K 12183:1968JChEd..45...45P 12146:2016PhRvB..93p5140J 12087:1964JChEd..41..354F 11868:1922ZPhy....9..353G 11802:1928Natur.121..580B 11755:1927ZPhy...43..172H 11720:on 27 November 2017 11550:on 27 November 2017 11494:1914Natur..93..268N 11452:1932PhRv...41...49M 11396:The Road to Reality 11178:Solid-state physics 10843:is oscillatory and 9659:. Higher values of 9484:{\displaystyle n=1} 8522:. The columns with 8479:{\displaystyle m=0} 7479:spherical harmonics 7316:spherical harmonics 5334: 5216: 5144: 5029: 4919:{\displaystyle z,r} 4723: 4525: 4440: 4254: 4171: 3993:s, p, d, f, g, h, i 3788: 3652: 3554: 2876: 2832: 2464:{\displaystyle n=2} 1691:The quantum number 1682:linear combinations 1330: = 1 and 1281:hydrogen-like atoms 1073:Slater-type orbital 975:spherical harmonics 759:Slater determinants 755:linear combinations 375:Electron properties 303:spectroscopic lines 267:. The simple names 163:charge distribution 99:probability density 12772:Dirac–Gordon model 12735:plum pudding model 12459:10.1007/BFb0116498 12371:(2037): 20140211. 12323:10.1007/BF01328209 12261:10.1007/BF01403504 11876:10.1007/BF01326984 11763:10.1007/BF01397280 11638:(extract of paper) 11316:Physical Chemistry 10925:spin–orbit effects 10833: 10792: 10768: 10197: 10180: 9808: 9788: 9765: 9745: 9721: 9695: 9669: 9649: 9629: 9581: 9561: 9541: 9521: 9501: 9481: 9455: 9443:hydrogen-like atom 9416: 9378: 9340: 9296: 9233: 9170: 9108: 9070: 9032: 8960: 8897: 8834: 8772: 8734: 8696: 8579: 8556: 8512: 8476: 7456:label). Also, the 7366:of the same shell 7356: 7303:possible value of 7194: 7143: 6824: 6791:Shapes of orbitals 6775: 6713: 6654: 6614: 6577: 6537: 6501: 6439: 6408: 6358: 6325: 6288: 6255: 6220: 6187: 6157: 6127: 6093: 6058: 6029: 6000: 5941: 5882: 5823: 5789: 5730: 5671: 5606: 5586: 5556: 5524: 5492: 5463: 5427: 5425: 5305: 5187: 5118: 5000: 4976: 4956: 4936: 4916: 4890: 4870: 4850: 4827: 4694: 4674: 4581: 4579: 4496: 4411: 4387: 4324: 4237: 4172: 4142: 4122: 4102: 4082: 4062: 3999: 3974: 3915: 3895: 3853: 3833: 3813: 3789: 3774: 3757: 3727: 3626: 3609: 3570: 3540: 3453: 3448: 3120: 2850: 2843:may be defined by 2833: 2806: 2789: 2769: 2749: 2729: 2690: 2678: 2649: 2487: 2461: 2435: 2415: 2395: 2375: 2210: 2117: 2087: 2045: 2018: 1990: 1948: 1922: 1889: 1856: 1768:spherical harmonic 1764: 1601:Hydrogen-like atom 1547: 1434: 1342:Immediately after 1252:absorption spectra 1236: 1184:plum pudding model 1143:Robert S. Mulliken 1112: 1058: 1025:hydrogen-like atom 882:coordinate systems 870: 800:summarized in the 723:quantum mechanical 695: 668: 648: 608: 581: 561: 537: 372: 257: 239:projection of spin 151:wave-like behavior 103: 13379:Quantum chemistry 13351: 13350: 13347: 13346: 13322:Constituent units 13303:Molecular orbital 13282: 13281: 13262:Constituent units 13222: 13221: 13096:Quantum mechanics 13045: 13044: 13023:Electron counting 12992:Unpaired electron 12868:Quantum mechanics 12813: 12812: 12743:(planetary model) 12730:(Saturnian model) 12630:10.1021/ed043p187 12600:978-0-13-111892-8 12581:978-0-321-80345-0 12572:Quantum Chemistry 12562:978-0-19-530573-9 12539:978-0-7167-4345-3 12468:978-3-540-07109-9 12430:10.1021/ed046p678 12226:10.1063/1.1750628 12134:Physical Review B 12095:10.1021/ed041p354 12008:978-0-321-80345-0 11999:Quantum Chemistry 11983:978-0-471-56952-7 11974:Quantum mechanics 11958:978-0-486-40924-5 11838:978-0-387-58080-7 11796:(3050): 580–590. 11682:978-0-684-81378-3 11588:978-0-7679-0818-4 11410:Quantum Chemistry 11377:978-0-8053-9046-9 11352:978-0-19-920606-3 11325:978-0-8053-5682-3 11300:978-0-13-685512-5 11286:Quantum Chemistry 11269:978-0-13-124405-4 11244:978-0-19-860918-6 11168:Quantum chemistry 11163:Molecular orbital 10889:period 8 elements 10689:valence electrons 10672: 10671: 10192: 10143: 10142: 9791:{\displaystyle n} 9768:{\displaystyle n} 9632:{\displaystyle n} 9584:{\displaystyle n} 9544:{\displaystyle n} 9524:{\displaystyle n} 9504:{\displaystyle n} 9458:{\displaystyle n} 9312:d-type drum modes 8503: 8415: 8414: 7417:orbital, but the 7256:point of tangency 6788: 6787: 6735: 6676: 6636: 6599: 6559: 6523: 6461: 6380: 6347: 6310: 6277: 6244: 6179: 6149: 6119: 6056: 5609:{\displaystyle g} 5545: 5513: 5484: 5455: 5376: 5375: 5332: 5285: 5264: 5250: 5249: 5229: 5214: 5175: 5157: 5142: 5098: 5077: 5063: 5062: 5042: 5027: 4986:quantum numbers. 4959:{\displaystyle n} 4939:{\displaystyle z} 4893:{\displaystyle z} 4873:{\displaystyle y} 4853:{\displaystyle x} 4825: 4768: 4767: 4751: 4721: 4658: 4575: 4562: 4561: 4523: 4490: 4477: 4476: 4438: 4385: 4293: 4169: 4125:{\displaystyle m} 4085:{\displaystyle n} 4023: 3994: 3856:{\displaystyle m} 3816:{\displaystyle n} 3650: 3435: 3329: 3328: 3304: 3252: 3146: 3145: 3107: 3060: 3036: 3016: 2964: 2917: 2893: 2874: 2830: 2792:{\displaystyle m} 2772:{\displaystyle l} 2752:{\displaystyle n} 2670: 2641: 2418:{\displaystyle n} 2378:{\displaystyle n} 2363: 2362: 1546: 1433: 1364:Erwin Schrödinger 1304:quantum mechanics 1266:quantum mechanics 1208:Ernest Rutherford 1164:quantum mechanics 1155:Ernest Rutherford 971:real combinations 860:3D views of some 671:{\displaystyle l} 651:{\displaystyle n} 584:{\displaystyle l} 564:{\displaystyle n} 540:{\displaystyle i} 381:quantum mechanics 107:quantum mechanics 16:(Redirected from 13386: 13369:Chemical bonding 13293: 13292: 13233: 13232: 13214:Exchange-coupled 13116: 13115: 13079:Chemical bonding 13072: 13065: 13058: 13049: 13048: 13037:18-electron rule 13008:Valence electron 12980:Electron pairing 12971:Aufbau principle 12954:Electron filling 12923: 12914: 12905: 12896: 12840: 12833: 12826: 12817: 12816: 12799: 12789: 12788: 12741:Rutherford model 12685: 12678: 12671: 12662: 12661: 12633: 12604: 12585: 12566: 12554: 12543: 12524: 12500: 12499: 12493: 12489: 12487: 12479: 12477: 12475: 12440: 12434: 12433: 12405: 12399: 12398: 12388: 12356: 12350: 12349: 12344:Lower, Stephen. 12341: 12335: 12334: 12293: 12287: 12286: 12280: 12272: 12236: 12230: 12229: 12201: 12195: 12194: 12191:10.1021/ed045p45 12166: 12160: 12159: 12157: 12125: 12116: 12115: 12105: 12099: 12098: 12070: 12064: 12063: 12046: 12040: 12039: 12019: 12013: 12012: 11994: 11988: 11987: 11969: 11963: 11962: 11944: 11938: 11937: 11919: 11913: 11912: 11894: 11888: 11887: 11849: 11843: 11842: 11822: 11816: 11815: 11813: 11811:10.1038/121580a0 11781: 11775: 11774: 11749:(3–4): 172–198. 11736: 11730: 11729: 11727: 11725: 11716:. Archived from 11693: 11687: 11686: 11666: 11660: 11659: 11639: 11630: 11624: 11623: 11599: 11593: 11592: 11576: 11566: 11560: 11559: 11557: 11555: 11546:. Archived from 11523: 11514: 11513: 11502:10.1038/093268a0 11473: 11464: 11463: 11433: 11427: 11426: 11405: 11399: 11388: 11382: 11381: 11363: 11357: 11356: 11336: 11330: 11329: 11311: 11305: 11304: 11280: 11274: 11273: 11255: 11249: 11248: 11228: 11222: 11221: 11219: 11208: 11199: 11138:Wiswesser's rule 11113: 11097: 11081: 11072: 11060: 11059: 11057: 11056: 11053: 11050: 11035: 11023: 11016: 11007: 11006: 11004: 11003: 11000: 10997: 10982: 10970: 10963: 10874: 10870: 10866: 10862: 10842: 10840: 10839: 10834: 10811: 10801: 10799: 10798: 10793: 10781: 10777: 10775: 10774: 10769: 10745: 10719: 10715: 10373: 10372: 10324: 10320: 10317:-state (but the 10316: 10274: 10272: 10271: 10268: 10265: 10258: 10256: 10255: 10252: 10249: 10242: 10235: 10228: 10193: 10176: 9822: 9821: 9817: 9815: 9814: 9809: 9797: 9795: 9794: 9789: 9774: 9772: 9771: 9766: 9754: 9752: 9751: 9746: 9730: 9728: 9727: 9722: 9704: 9702: 9701: 9696: 9678: 9676: 9675: 9670: 9658: 9656: 9655: 9650: 9638: 9636: 9635: 9630: 9598: 9594: 9590: 9588: 9587: 9582: 9570: 9568: 9567: 9562: 9550: 9548: 9547: 9542: 9530: 9528: 9527: 9522: 9510: 9508: 9507: 9502: 9490: 9488: 9487: 9482: 9464: 9462: 9461: 9456: 9425: 9423: 9422: 9417: 9415: 9414: 9396: 9387: 9385: 9384: 9379: 9377: 9376: 9358: 9349: 9347: 9346: 9341: 9339: 9338: 9320: 9305: 9303: 9302: 9297: 9295: 9294: 9279: 9278: 9277: 9252: 9242: 9240: 9239: 9234: 9232: 9231: 9216: 9215: 9214: 9189: 9179: 9177: 9176: 9171: 9169: 9168: 9153: 9152: 9151: 9126: 9117: 9115: 9114: 9109: 9107: 9106: 9088: 9079: 9077: 9076: 9071: 9069: 9068: 9050: 9041: 9039: 9038: 9033: 9031: 9030: 9012: 8969: 8967: 8966: 8961: 8959: 8958: 8943: 8942: 8941: 8916: 8906: 8904: 8903: 8898: 8896: 8895: 8880: 8879: 8878: 8853: 8843: 8841: 8840: 8835: 8833: 8832: 8817: 8816: 8815: 8790: 8781: 8779: 8778: 8773: 8771: 8770: 8752: 8743: 8741: 8740: 8735: 8733: 8732: 8714: 8705: 8703: 8702: 8697: 8695: 8694: 8676: 8663: 8647: 8565: 8563: 8562: 8557: 8521: 8519: 8518: 8513: 8511: 8510: 8505: 8504: 8496: 8485: 8483: 8482: 8477: 8321: 8314: 8232: 8225: 8218: 8211: 8204: 8159: 8152: 8145: 8138: 8131: 8124: 8117: 8110: 8103: 8096: 8086: 8079: 8072: 8065: 8058: 8051: 8044: 8037: 8030: 8023: 8016: 8009: 8002: 7995: 7988: 7981: 7974: 7950: 7943: 7936: 7929: 7922: 7915: 7908: 7901: 7894: 7887: 7853: 7846: 7839: 7832: 7825: 7785: 7778: 7610: 7602: 7594: 7586: 7578: 7570: 7562: 7554: 7546: 7538: 7525: 7515: 7505: 7495: 7484: 7483: 7476: 7469: 7462: 7455: 7448: 7441: 7434: 7425: 7416: 7409: 7376:Unsöld's theorem 7373: 7369: 7365: 7346: 7337: 7310: 7306: 7301: 7286: 7276: 7249: 7225: 7221: 7211:it is roughly a 7210: 7203: 7201: 7200: 7195: 7174: 7170: 7166: 7155: 7148: 7132: 7128: 7124: 7118:is orientation. 7117: 7110:is analogous to 7109: 7105: 7101: 7097: 7093: 7089: 7082: 7075: 7071: 7067: 7063: 7046: 7035: 7028: 7016: 7004: 7000: 6996: 6989: 6972: 6956: 6940: 6938: 6916: 6900: 6884: 6877: 6854: 6846: 6829:contour surfaces 6821: 6814: 6784: 6782: 6781: 6776: 6774: 6773: 6769: 6768: 6753: 6752: 6736: 6733: 6722: 6720: 6719: 6714: 6712: 6711: 6707: 6706: 6694: 6693: 6677: 6674: 6663: 6661: 6660: 6655: 6653: 6652: 6651: 6650: 6637: 6634: 6623: 6621: 6620: 6615: 6613: 6612: 6611: 6610: 6600: 6597: 6586: 6584: 6583: 6578: 6576: 6575: 6574: 6573: 6560: 6557: 6546: 6544: 6543: 6538: 6536: 6535: 6524: 6521: 6510: 6508: 6507: 6502: 6500: 6499: 6495: 6494: 6482: 6481: 6462: 6459: 6448: 6446: 6445: 6440: 6417: 6415: 6414: 6409: 6407: 6406: 6405: 6404: 6392: 6391: 6381: 6378: 6367: 6365: 6364: 6359: 6357: 6356: 6348: 6345: 6334: 6332: 6331: 6326: 6324: 6323: 6322: 6321: 6311: 6308: 6297: 6295: 6294: 6289: 6287: 6286: 6278: 6275: 6264: 6262: 6261: 6256: 6254: 6253: 6245: 6242: 6229: 6227: 6226: 6221: 6196: 6194: 6193: 6188: 6186: 6185: 6180: 6177: 6166: 6164: 6163: 6158: 6156: 6155: 6150: 6147: 6136: 6134: 6133: 6128: 6126: 6125: 6120: 6117: 6102: 6100: 6099: 6094: 6067: 6065: 6064: 6059: 6057: 6054: 6038: 6036: 6035: 6030: 6009: 6007: 6006: 6001: 5999: 5998: 5977: 5976: 5950: 5948: 5947: 5942: 5940: 5939: 5918: 5917: 5891: 5889: 5888: 5883: 5881: 5880: 5859: 5858: 5832: 5830: 5829: 5824: 5822: 5821: 5798: 5796: 5795: 5790: 5788: 5787: 5766: 5765: 5739: 5737: 5736: 5731: 5729: 5728: 5707: 5706: 5680: 5678: 5677: 5672: 5670: 5669: 5648: 5647: 5619: 5618: 5615: 5613: 5612: 5607: 5595: 5593: 5592: 5587: 5565: 5563: 5562: 5557: 5555: 5554: 5546: 5543: 5533: 5531: 5530: 5525: 5523: 5522: 5514: 5511: 5501: 5499: 5498: 5493: 5491: 5490: 5485: 5482: 5472: 5470: 5469: 5464: 5462: 5461: 5456: 5453: 5436: 5434: 5433: 5428: 5426: 5422: 5418: 5417: 5416: 5398: 5397: 5377: 5371: 5367: 5362: 5361: 5360: 5359: 5333: 5330: 5328: 5300: 5296: 5295: 5294: 5286: 5283: 5274: 5273: 5265: 5262: 5251: 5245: 5241: 5236: 5235: 5230: 5227: 5215: 5212: 5210: 5182: 5181: 5176: 5173: 5164: 5163: 5158: 5155: 5143: 5140: 5138: 5113: 5109: 5108: 5107: 5099: 5096: 5087: 5086: 5078: 5075: 5064: 5058: 5054: 5049: 5048: 5043: 5040: 5028: 5025: 5023: 4985: 4983: 4982: 4977: 4965: 4963: 4962: 4957: 4945: 4943: 4942: 4937: 4925: 4923: 4922: 4917: 4899: 4897: 4896: 4891: 4879: 4877: 4876: 4871: 4859: 4857: 4856: 4851: 4836: 4834: 4833: 4828: 4826: 4824: 4823: 4814: 4810: 4809: 4797: 4796: 4774: 4769: 4766: 4755: 4754: 4752: 4744: 4742: 4741: 4722: 4719: 4717: 4683: 4681: 4680: 4675: 4670: 4659: 4651: 4643: 4641: 4640: 4622: 4621: 4590: 4588: 4587: 4582: 4580: 4576: 4568: 4563: 4560: 4549: 4548: 4546: 4545: 4524: 4521: 4519: 4491: 4483: 4478: 4475: 4464: 4463: 4461: 4460: 4439: 4436: 4434: 4396: 4394: 4393: 4388: 4386: 4384: 4383: 4371: 4370: 4358: 4357: 4348: 4333: 4331: 4330: 4325: 4320: 4294: 4286: 4278: 4276: 4275: 4253: 4245: 4236: 4235: 4217: 4216: 4181: 4179: 4178: 4173: 4170: 4167: 4165: 4132:quantum number. 4131: 4129: 4128: 4123: 4111: 4109: 4108: 4103: 4091: 4089: 4088: 4083: 4071: 4069: 4068: 4063: 4061: 4060: 4033: 4032: 4024: 4021: 4008: 4006: 4005: 4000: 3995: 3992: 3983: 3981: 3980: 3975: 3924: 3922: 3921: 3916: 3904: 3902: 3901: 3896: 3894: 3893: 3862: 3860: 3859: 3854: 3842: 3840: 3839: 3834: 3822: 3820: 3819: 3814: 3798: 3796: 3795: 3790: 3787: 3782: 3766: 3764: 3763: 3758: 3756: 3755: 3736: 3734: 3733: 3728: 3711: 3710: 3689: 3688: 3651: 3648: 3646: 3618: 3616: 3615: 3610: 3599: 3598: 3579: 3577: 3576: 3571: 3553: 3548: 3530: 3529: 3493: 3492: 3462: 3460: 3459: 3454: 3452: 3451: 3436: 3433: 3429: 3425: 3424: 3423: 3422: 3414: 3392: 3391: 3370: 3369: 3368: 3360: 3330: 3324: 3320: 3305: 3302: 3298: 3297: 3296: 3288: 3253: 3250: 3246: 3242: 3241: 3240: 3239: 3231: 3209: 3208: 3187: 3186: 3185: 3177: 3147: 3141: 3137: 3124: 3123: 3108: 3105: 3101: 3097: 3096: 3095: 3087: 3061: 3058: 3056: 3055: 3037: 3032: 3017: 3014: 3010: 3009: 3008: 3000: 2965: 2962: 2958: 2954: 2953: 2952: 2944: 2918: 2915: 2913: 2912: 2894: 2889: 2875: 2872: 2870: 2842: 2840: 2839: 2834: 2831: 2828: 2826: 2798: 2796: 2795: 2790: 2778: 2776: 2775: 2770: 2758: 2756: 2755: 2750: 2738: 2736: 2735: 2730: 2728: 2727: 2687: 2685: 2684: 2679: 2677: 2676: 2671: 2668: 2658: 2656: 2655: 2650: 2648: 2647: 2642: 2639: 2613: 2606: 2585: 2581: 2577: 2566: 2564: 2563: 2560: 2557: 2550: 2548: 2547: 2544: 2541: 2535:, which can be + 2523: 2521: 2520: 2517: 2514: 2496: 2494: 2493: 2488: 2470: 2468: 2467: 2462: 2444: 2442: 2441: 2436: 2424: 2422: 2421: 2416: 2404: 2402: 2401: 2396: 2384: 2382: 2381: 2376: 2318: 2291: 2274:−2, −1, 0, 1, 2 2265: 2240: 2219: 2217: 2216: 2211: 2203: 2202: 2185: 2172: 2164: 2156: 2148: 2140: 2130: 2129: 2126: 2124: 2123: 2118: 2116: 2115: 2096: 2094: 2093: 2088: 2080: 2079: 2054: 2052: 2051: 2046: 2044: 2043: 2027: 2025: 2024: 2019: 1999: 1997: 1996: 1991: 1989: 1988: 1961: 1957: 1955: 1954: 1949: 1931: 1929: 1928: 1923: 1905: 1898: 1896: 1895: 1890: 1872: 1865: 1863: 1862: 1857: 1849: 1848: 1820: 1816: 1808:is some integer 1807: 1803: 1782:positive integer 1779: 1754:Complex orbitals 1722: 1702: 1694: 1668: 1659: 1653: 1590: 1565: 1556: 1554: 1553: 1548: 1544: 1543: 1542: 1537: 1504: 1497: 1490: 1483: 1473: 1457: 1443: 1441: 1440: 1435: 1431: 1430: 1121: 1119: 1118: 1113: 1111: 1110: 1109: 1108: 1078:The form of the 1067: 1065: 1064: 1059: 1057: 1056: 1014: 1003: 999: 995: 968: 956: 921: 902: 852:Types of orbital 704: 702: 701: 696: 694: 693: 677: 675: 674: 669: 657: 655: 654: 649: 633: 631: 630: 627: 624: 617: 615: 614: 609: 607: 606: 590: 588: 587: 582: 570: 568: 567: 562: 546: 544: 543: 538: 527: 525: 524: 521: 518: 511: 509: 508: 505: 502: 495: 493: 492: 489: 486: 479: 477: 476: 473: 470: 458:weighted average 354: 327: 293: 289: 266: 264: 263: 258: 256: 255: 233: 215: 208: 193: 186: 182: 144: 143: 140: 139: 136: 133: 130: 127: 124: 121: 96: 80: 21: 13394: 13393: 13389: 13388: 13387: 13385: 13384: 13383: 13374:Electron states 13354: 13353: 13352: 13343: 13317: 13278: 13257: 13253:Lewis structure 13218: 13189: 13145: 13107: 13082: 13076: 13046: 13041: 13017: 12996: 12975: 12949: 12928: 12921: 12912: 12903: 12894: 12885:Quantum numbers 12879: 12849: 12844: 12814: 12809: 12777: 12753: 12699:Historic models 12694: 12689: 12640: 12601: 12582: 12563: 12540: 12521: 12503: 12491: 12490: 12481: 12480: 12473: 12471: 12469: 12441: 12437: 12406: 12402: 12357: 12353: 12342: 12338: 12294: 12290: 12274: 12273: 12237: 12233: 12202: 12198: 12167: 12163: 12126: 12119: 12106: 12102: 12071: 12067: 12060: 12048: 12047: 12043: 12020: 12016: 12009: 11995: 11991: 11984: 11970: 11966: 11959: 11945: 11941: 11934: 11920: 11916: 11909: 11895: 11891: 11850: 11846: 11839: 11823: 11819: 11782: 11778: 11737: 11733: 11723: 11721: 11694: 11690: 11683: 11667: 11663: 11650:(39): 237–265. 11637: 11631: 11627: 11600: 11596: 11589: 11567: 11563: 11553: 11551: 11538:(41): 445–455. 11524: 11517: 11474: 11467: 11439:Physical Review 11434: 11430: 11420: 11406: 11402: 11389: 11385: 11378: 11364: 11360: 11353: 11337: 11333: 11326: 11312: 11308: 11301: 11281: 11277: 11270: 11256: 11252: 11245: 11229: 11225: 11217: 11206: 11200: 11196: 11192: 11187: 11128: 11112: 11105: 11099: 11096: 11089: 11083: 11080: 11074: 11071: 11065: 11054: 11051: 11048: 11047: 11045: 11042: 11037: 11033: 11025: 11018: 11011: 11001: 10998: 10995: 10994: 10992: 10989: 10984: 10980: 10972: 10965: 10958: 10947: 10941: 10922: 10918: 10902: 10898: 10885: 10872: 10868: 10867:. The critical 10864: 10860: 10853:Richard Feynman 10822: 10819: 10818: 10807: 10787: 10784: 10783: 10779: 10751: 10748: 10747: 10740: 10717: 10713: 10710: 10704: 10698: 10322: 10318: 10314: 10269: 10266: 10263: 10262: 10260: 10253: 10250: 10247: 10246: 10244: 10241: 10237: 10234: 10230: 10227: 10223: 10207: 10199:Main articles: 10182: 10174: 10153: 9834: 9829: 9803: 9800: 9799: 9783: 9780: 9779: 9760: 9757: 9756: 9740: 9737: 9736: 9710: 9707: 9706: 9684: 9681: 9680: 9664: 9661: 9660: 9644: 9641: 9640: 9624: 9621: 9620: 9596: 9592: 9576: 9573: 9572: 9571:within a given 9556: 9553: 9552: 9536: 9533: 9532: 9516: 9513: 9512: 9496: 9493: 9492: 9470: 9467: 9466: 9450: 9447: 9446: 9439: 9433: 9426: 9410: 9406: 9404: 9401: 9400: 9397: 9388: 9372: 9368: 9366: 9363: 9362: 9359: 9350: 9334: 9330: 9328: 9325: 9324: 9321: 9307: 9290: 9286: 9267: 9266: 9262: 9260: 9257: 9256: 9253: 9244: 9227: 9223: 9204: 9203: 9199: 9197: 9194: 9193: 9190: 9181: 9164: 9160: 9141: 9140: 9136: 9134: 9131: 9130: 9127: 9118: 9102: 9098: 9096: 9093: 9092: 9089: 9080: 9064: 9060: 9058: 9055: 9054: 9051: 9042: 9026: 9022: 9020: 9017: 9016: 9013: 8971: 8954: 8950: 8931: 8930: 8926: 8924: 8921: 8920: 8917: 8908: 8891: 8887: 8868: 8867: 8863: 8861: 8858: 8857: 8854: 8845: 8828: 8824: 8805: 8804: 8800: 8798: 8795: 8794: 8791: 8782: 8766: 8762: 8760: 8757: 8756: 8753: 8744: 8728: 8724: 8722: 8719: 8718: 8715: 8706: 8690: 8686: 8684: 8681: 8680: 8677: 8649: 8637: 8618:Keplerian orbit 8584: 8527: 8524: 8523: 8506: 8495: 8494: 8493: 8491: 8488: 8487: 8465: 8462: 8461: 8309: 8199: 8091: 7969: 7882: 7820: 7773: 7768: 7751: 7734: 7717: 7709: 7701: 7693: 7685: 7673: 7665: 7657: 7649: 7641: 7633: 7625: 7605: 7597: 7589: 7581: 7573: 7565: 7557: 7549: 7541: 7533: 7520: 7510: 7500: 7490: 7475: 7471: 7468: 7464: 7461: 7457: 7450: 7447: 7443: 7440: 7436: 7433: 7427: 7424: 7418: 7415: 7411: 7408: 7402: 7384: 7371: 7367: 7363: 7360:Albrecht Unsöld 7345: 7339: 7335: 7329: 7323: 7320:cubic harmonics 7308: 7304: 7299: 7281: 7275: 7271: 7244: 7234: 7223: 7216: 7205: 7183: 7180: 7179: 7172: 7168: 7165: 7161: 7158:complex numbers 7154: 7150: 7146: 7130: 7126: 7122: 7115: 7107: 7103: 7099: 7095: 7091: 7084: 7077: 7073: 7069: 7065: 7061: 7041: 7030: 7018: 7006: 7002: 6998: 6991: 6987: 6958: 6942: 6924: 6922: 6902: 6886: 6882: 6863: 6848: 6832: 6816: 6800: 6793: 6764: 6760: 6748: 6744: 6737: 6732: 6731: 6729: 6726: 6725: 6702: 6698: 6689: 6685: 6678: 6673: 6672: 6670: 6667: 6666: 6646: 6642: 6638: 6633: 6632: 6630: 6627: 6626: 6606: 6602: 6601: 6596: 6595: 6593: 6590: 6589: 6569: 6565: 6561: 6556: 6555: 6553: 6550: 6549: 6525: 6520: 6519: 6517: 6514: 6513: 6490: 6486: 6477: 6473: 6463: 6458: 6457: 6455: 6452: 6451: 6428: 6425: 6424: 6400: 6396: 6387: 6383: 6382: 6377: 6376: 6374: 6371: 6370: 6349: 6344: 6343: 6341: 6338: 6337: 6317: 6313: 6312: 6307: 6306: 6304: 6301: 6300: 6279: 6274: 6273: 6271: 6268: 6267: 6246: 6241: 6240: 6238: 6235: 6234: 6209: 6206: 6205: 6181: 6176: 6175: 6173: 6170: 6169: 6151: 6146: 6145: 6143: 6140: 6139: 6121: 6116: 6115: 6113: 6110: 6109: 6082: 6079: 6078: 6053: 6051: 6048: 6047: 6018: 6015: 6014: 5985: 5981: 5963: 5959: 5957: 5954: 5953: 5926: 5922: 5904: 5900: 5898: 5895: 5894: 5867: 5863: 5845: 5841: 5839: 5836: 5835: 5811: 5807: 5805: 5802: 5801: 5774: 5770: 5752: 5748: 5746: 5743: 5742: 5715: 5711: 5693: 5689: 5687: 5684: 5683: 5656: 5652: 5634: 5630: 5628: 5625: 5624: 5601: 5598: 5597: 5575: 5572: 5571: 5547: 5542: 5541: 5539: 5536: 5535: 5515: 5510: 5509: 5507: 5504: 5503: 5486: 5481: 5480: 5478: 5475: 5474: 5457: 5452: 5451: 5449: 5446: 5445: 5424: 5423: 5409: 5405: 5390: 5386: 5382: 5378: 5366: 5355: 5351: 5347: 5343: 5338: 5329: 5309: 5302: 5301: 5287: 5282: 5281: 5266: 5261: 5260: 5256: 5252: 5240: 5231: 5226: 5225: 5220: 5211: 5191: 5184: 5183: 5177: 5172: 5171: 5159: 5154: 5153: 5148: 5139: 5122: 5115: 5114: 5100: 5095: 5094: 5079: 5074: 5073: 5069: 5065: 5053: 5044: 5039: 5038: 5033: 5024: 5004: 4996: 4994: 4991: 4990: 4971: 4968: 4967: 4951: 4948: 4947: 4931: 4928: 4927: 4905: 4902: 4901: 4885: 4882: 4881: 4865: 4862: 4861: 4845: 4842: 4841: 4819: 4815: 4805: 4801: 4792: 4788: 4775: 4773: 4759: 4753: 4743: 4731: 4727: 4718: 4698: 4692: 4689: 4688: 4666: 4647: 4642: 4630: 4626: 4605: 4601: 4599: 4596: 4595: 4578: 4577: 4567: 4553: 4547: 4535: 4531: 4529: 4520: 4500: 4493: 4492: 4482: 4468: 4462: 4450: 4446: 4444: 4435: 4415: 4407: 4405: 4402: 4401: 4379: 4375: 4366: 4362: 4353: 4349: 4347: 4339: 4336: 4335: 4316: 4282: 4277: 4265: 4261: 4246: 4241: 4225: 4221: 4197: 4193: 4191: 4188: 4187: 4166: 4146: 4140: 4137: 4136: 4117: 4114: 4113: 4097: 4094: 4093: 4077: 4074: 4073: 4041: 4037: 4025: 4020: 4019: 4014: 4011: 4010: 3991: 3989: 3986: 3985: 3930: 3927: 3926: 3910: 3907: 3906: 3877: 3873: 3871: 3868: 3867: 3848: 3845: 3844: 3828: 3825: 3824: 3808: 3805: 3804: 3783: 3778: 3772: 3769: 3768: 3748: 3744: 3742: 3739: 3738: 3703: 3699: 3681: 3677: 3647: 3630: 3624: 3621: 3620: 3591: 3587: 3585: 3582: 3581: 3549: 3544: 3522: 3518: 3476: 3472: 3470: 3467: 3466: 3447: 3446: 3434: for 3432: 3430: 3418: 3410: 3397: 3393: 3387: 3383: 3364: 3356: 3340: 3336: 3335: 3331: 3319: 3316: 3315: 3303: for 3301: 3299: 3292: 3284: 3271: 3267: 3264: 3263: 3251: for 3249: 3247: 3235: 3227: 3214: 3210: 3204: 3200: 3181: 3173: 3157: 3153: 3152: 3148: 3136: 3129: 3128: 3119: 3118: 3106: for 3104: 3102: 3091: 3083: 3070: 3066: 3062: 3057: 3051: 3047: 3031: 3028: 3027: 3015: for 3013: 3011: 3004: 2996: 2983: 2979: 2976: 2975: 2963: for 2961: 2959: 2948: 2940: 2927: 2923: 2919: 2914: 2908: 2904: 2888: 2881: 2880: 2871: 2854: 2848: 2845: 2844: 2827: 2810: 2804: 2801: 2800: 2784: 2781: 2780: 2764: 2761: 2760: 2744: 2741: 2740: 2711: 2707: 2705: 2702: 2701: 2672: 2667: 2666: 2664: 2661: 2660: 2643: 2638: 2637: 2635: 2632: 2631: 2624: 2608: 2601: 2591: 2583: 2579: 2575: 2561: 2558: 2555: 2554: 2552: 2545: 2542: 2539: 2538: 2536: 2533: 2518: 2515: 2512: 2511: 2509: 2476: 2473: 2472: 2450: 2447: 2446: 2430: 2427: 2426: 2410: 2407: 2406: 2390: 2387: 2386: 2370: 2367: 2366: 2327:−2, −1, 0, 1, 2 2313: 2300:−2, −1, 0, 1, 2 2286: 2260: 2235: 2198: 2194: 2192: 2189: 2188: 2180: 2167: 2159: 2151: 2143: 2135: 2111: 2107: 2105: 2102: 2101: 2075: 2071: 2060: 2057: 2056: 2039: 2035: 2033: 2030: 2029: 2013: 2010: 2009: 1984: 1980: 1978: 1975: 1974: 1959: 1937: 1934: 1933: 1911: 1908: 1907: 1900: 1878: 1875: 1874: 1867: 1844: 1840: 1826: 1823: 1822: 1818: 1815: 1809: 1805: 1801: 1791:electron shells 1777: 1756: 1739: 1733: 1731:Quantum numbers 1720: 1700: 1692: 1666: 1661: 1655: 1649: 1603: 1597: 1585: 1578: 1572: 1563: 1538: 1524: 1523: 1517: 1514: 1513: 1502: 1492: 1485: 1478: 1471: 1455: 1417: 1411: 1408: 1407: 1401: 1396: 1346:discovered his 1340: 1308:electron shells 1204: 1196:Saturnian model 1191:Hantaro Nagaoka 1172: 1162:development of 1159:Hantaro Nagaoka 1139: 1133: 1104: 1100: 1093: 1089: 1087: 1084: 1083: 1046: 1042: 1040: 1037: 1036: 1005: 1001: 997: 985: 977: 958: 923: 907: 888: 854: 811: 808:-term symbol: S 798:quantum numbers 719: 689: 685: 683: 680: 679: 663: 660: 659: 643: 640: 639: 628: 625: 622: 621: 619: 602: 598: 596: 593: 592: 576: 573: 572: 556: 553: 552: 532: 529: 528: 522: 519: 516: 515: 513: 506: 503: 500: 499: 497: 490: 487: 484: 483: 481: 474: 471: 468: 467: 465: 377: 352: 322: 321:. Orbitals for 291: 284: 251: 247: 245: 242: 241: 225: 214: 210: 207: 203: 192: 188: 184: 180: 178:quantum numbers 118: 114: 82: 66: 63:domain coloring 60: 54: 48: 35: 28: 23: 22: 15: 12: 11: 5: 13392: 13382: 13381: 13376: 13371: 13366: 13364:Atomic physics 13349: 13348: 13345: 13344: 13342: 13341: 13339:Antibonding MO 13336: 13334:Non-bonding MO 13331: 13325: 13323: 13319: 13318: 13316: 13315: 13310: 13305: 13299: 13297: 13290: 13284: 13283: 13280: 13279: 13277: 13276: 13271: 13265: 13263: 13259: 13258: 13256: 13255: 13250: 13245: 13243:Hybrid orbital 13239: 13237: 13230: 13224: 13223: 13220: 13219: 13217: 13216: 13211: 13206: 13200: 13198: 13191: 13190: 13188: 13187: 13182: 13177: 13172: 13167: 13162: 13156: 13154: 13147: 13146: 13144: 13143: 13138: 13133: 13128: 13122: 13120: 13113: 13112:Types of bonds 13109: 13108: 13106: 13105: 13104: 13103: 13093: 13091:Atomic orbital 13087: 13084: 13083: 13075: 13074: 13067: 13060: 13052: 13043: 13042: 13040: 13039: 13034: 13028: 13026: 13019: 13018: 13016: 13015: 13010: 13004: 13002: 12998: 12997: 12995: 12994: 12989: 12983: 12981: 12977: 12976: 12974: 12973: 12968: 12963: 12957: 12955: 12951: 12950: 12948: 12947: 12942: 12936: 12934: 12930: 12929: 12927: 12926: 12917: 12908: 12899: 12889: 12887: 12881: 12880: 12878: 12877: 12876: 12875: 12865: 12863:Atomic orbital 12860: 12858:Electron shell 12854: 12851: 12850: 12843: 12842: 12835: 12828: 12820: 12811: 12810: 12808: 12807: 12801:Portal:Physics 12793: 12791:Category:Atoms 12782: 12779: 12778: 12776: 12775: 12768: 12761: 12759: 12758:Current models 12755: 12754: 12752: 12751: 12744: 12737: 12731: 12724: 12717: 12710: 12702: 12700: 12696: 12695: 12688: 12687: 12680: 12673: 12665: 12659: 12658: 12652: 12646: 12639: 12638:External links 12636: 12635: 12634: 12605: 12599: 12586: 12580: 12567: 12561: 12544: 12538: 12530:Modern Physics 12525: 12519: 12502: 12501: 12492:|journal= 12467: 12435: 12400: 12351: 12336: 12288: 12247:(4): 549–561. 12231: 12196: 12161: 12140:(16): 165140. 12117: 12100: 12065: 12059:978-0133897319 12058: 12041: 12030:(1–3): 19–27. 12014: 12007: 11989: 11982: 11964: 11957: 11939: 11933:978-0133897319 11932: 11914: 11908:978-0387207773 11907: 11889: 11862:(1): 353–355. 11844: 11837: 11817: 11776: 11731: 11688: 11681: 11661: 11625: 11604:"Cathode rays" 11594: 11587: 11561: 11515: 11465: 11428: 11418: 11400: 11383: 11376: 11358: 11351: 11331: 11324: 11306: 11299: 11275: 11268: 11250: 11243: 11223: 11193: 11191: 11188: 11186: 11185: 11180: 11175: 11170: 11165: 11160: 11155: 11150: 11145: 11140: 11135: 11129: 11127: 11124: 11110: 11103: 11094: 11087: 11078: 11069: 11062: 11061: 11040: 11029: 11008: 10987: 10976: 10943:Main article: 10940: 10937: 10920: 10916: 10913:valence shells 10900: 10896: 10884: 10881: 10832: 10829: 10826: 10815:Dirac equation 10791: 10767: 10764: 10761: 10758: 10755: 10700:Main article: 10697: 10694: 10670: 10669: 10666: 10663: 10660: 10657: 10654: 10651: 10648: 10645: 10642: 10639: 10636: 10633: 10630: 10627: 10624: 10620: 10619: 10616: 10613: 10610: 10607: 10604: 10601: 10598: 10595: 10592: 10589: 10586: 10583: 10580: 10577: 10574: 10570: 10569: 10566: 10563: 10560: 10557: 10554: 10551: 10548: 10545: 10543: 10541: 10539: 10537: 10535: 10533: 10531: 10527: 10526: 10523: 10520: 10517: 10514: 10511: 10508: 10505: 10502: 10500: 10498: 10496: 10494: 10492: 10490: 10488: 10484: 10483: 10480: 10477: 10474: 10472: 10470: 10468: 10466: 10464: 10462: 10460: 10458: 10456: 10454: 10452: 10450: 10446: 10445: 10442: 10439: 10436: 10434: 10432: 10430: 10428: 10426: 10424: 10422: 10420: 10418: 10416: 10414: 10412: 10408: 10407: 10405: 10403: 10401: 10399: 10397: 10395: 10393: 10391: 10389: 10387: 10385: 10383: 10381: 10379: 10377: 10352: 10351: 10288:periodic table 10239: 10232: 10225: 10205:Electron shell 10152: 10149: 10141: 10140: 10135: 10130: 10125: 10120: 10115: 10110: 10104: 10103: 10098: 10093: 10088: 10083: 10078: 10073: 10067: 10066: 10061: 10056: 10051: 10046: 10041: 10036: 10030: 10029: 10024: 10019: 10014: 10009: 10006: 10003: 9997: 9996: 9991: 9986: 9981: 9978: 9975: 9972: 9966: 9965: 9963: 9958: 9955: 9952: 9949: 9946: 9940: 9939: 9937: 9935: 9932: 9929: 9926: 9923: 9917: 9916: 9914: 9912: 9910: 9907: 9904: 9901: 9895: 9894: 9892: 9890: 9888: 9886: 9883: 9880: 9874: 9873: 9871: 9869: 9867: 9865: 9863: 9860: 9854: 9853: 9850: 9847: 9844: 9841: 9838: 9835: 9830: 9825: 9807: 9787: 9764: 9744: 9720: 9717: 9714: 9694: 9691: 9688: 9668: 9648: 9628: 9580: 9560: 9540: 9520: 9500: 9480: 9477: 9474: 9454: 9437:Electron shell 9435:Main article: 9432: 9431:Orbital energy 9429: 9428: 9427: 9413: 9409: 9398: 9391: 9389: 9375: 9371: 9360: 9353: 9351: 9337: 9333: 9322: 9315: 9313: 9309: 9308: 9293: 9289: 9285: 9282: 9276: 9273: 9270: 9265: 9254: 9247: 9245: 9230: 9226: 9222: 9219: 9213: 9210: 9207: 9202: 9191: 9184: 9182: 9167: 9163: 9159: 9156: 9150: 9147: 9144: 9139: 9128: 9121: 9119: 9105: 9101: 9090: 9083: 9081: 9067: 9063: 9052: 9045: 9043: 9029: 9025: 9014: 9007: 9005: 8973: 8972: 8957: 8953: 8949: 8946: 8940: 8937: 8934: 8929: 8918: 8911: 8909: 8894: 8890: 8886: 8883: 8877: 8874: 8871: 8866: 8855: 8848: 8846: 8831: 8827: 8823: 8820: 8814: 8811: 8808: 8803: 8792: 8785: 8783: 8769: 8765: 8754: 8747: 8745: 8731: 8727: 8716: 8709: 8707: 8693: 8689: 8678: 8671: 8669: 8583: 8580: 8555: 8552: 8549: 8546: 8543: 8540: 8537: 8534: 8531: 8509: 8502: 8499: 8475: 8472: 8469: 8413: 8412: 8406: 8400: 8394: 8388: 8382: 8376: 8370: 8364: 8358: 8352: 8346: 8340: 8334: 8328: 8322: 8315: 8306: 8305: 8299: 8293: 8287: 8281: 8275: 8269: 8263: 8257: 8251: 8245: 8239: 8233: 8226: 8219: 8212: 8205: 8196: 8195: 8190: 8185: 8180: 8175: 8170: 8165: 8160: 8153: 8146: 8139: 8132: 8125: 8118: 8111: 8104: 8097: 8088: 8087: 8080: 8073: 8066: 8059: 8052: 8045: 8038: 8031: 8024: 8017: 8010: 8003: 7996: 7989: 7982: 7975: 7966: 7965: 7963: 7961: 7959: 7957: 7955: 7953: 7951: 7944: 7937: 7930: 7923: 7916: 7909: 7902: 7895: 7888: 7879: 7878: 7876: 7874: 7872: 7870: 7868: 7866: 7864: 7862: 7860: 7858: 7856: 7854: 7847: 7840: 7833: 7826: 7817: 7816: 7814: 7812: 7810: 7808: 7806: 7804: 7802: 7800: 7798: 7796: 7794: 7792: 7790: 7788: 7786: 7779: 7770: 7769: 7755: 7752: 7738: 7735: 7721: 7718: 7713: 7710: 7705: 7702: 7697: 7694: 7689: 7686: 7677: 7674: 7669: 7666: 7661: 7658: 7653: 7650: 7645: 7642: 7637: 7634: 7629: 7626: 7621: 7618: 7615: 7612: 7611: 7603: 7595: 7587: 7579: 7571: 7563: 7555: 7547: 7539: 7531: 7528: 7527: 7517: 7507: 7497: 7487: 7473: 7466: 7459: 7445: 7438: 7429: 7420: 7413: 7404: 7383: 7382:Orbitals table 7380: 7341: 7331: 7325: 7273: 7241:Orbitals table 7232: 7193: 7190: 7187: 7163: 7152: 6985:traveling wave 6919:complex number 6881:Sometimes the 6857:absolute value 6792: 6789: 6786: 6785: 6772: 6767: 6763: 6759: 6756: 6751: 6747: 6743: 6740: 6723: 6710: 6705: 6701: 6697: 6692: 6688: 6684: 6681: 6664: 6649: 6645: 6641: 6624: 6609: 6605: 6587: 6572: 6568: 6564: 6547: 6534: 6531: 6528: 6511: 6498: 6493: 6489: 6485: 6480: 6476: 6472: 6469: 6466: 6449: 6438: 6435: 6432: 6421: 6420: 6418: 6403: 6399: 6395: 6390: 6386: 6368: 6355: 6352: 6335: 6320: 6316: 6298: 6285: 6282: 6265: 6252: 6249: 6232: 6230: 6219: 6216: 6213: 6202: 6201: 6199: 6197: 6184: 6167: 6154: 6137: 6124: 6107: 6105: 6103: 6092: 6089: 6086: 6075: 6074: 6072: 6070: 6068: 6045: 6043: 6041: 6039: 6028: 6025: 6022: 6011: 6010: 5997: 5994: 5991: 5988: 5984: 5980: 5975: 5972: 5969: 5966: 5962: 5951: 5938: 5935: 5932: 5929: 5925: 5921: 5916: 5913: 5910: 5907: 5903: 5892: 5879: 5876: 5873: 5870: 5866: 5862: 5857: 5854: 5851: 5848: 5844: 5833: 5820: 5817: 5814: 5810: 5799: 5786: 5783: 5780: 5777: 5773: 5769: 5764: 5761: 5758: 5755: 5751: 5740: 5727: 5724: 5721: 5718: 5714: 5710: 5705: 5702: 5699: 5696: 5692: 5681: 5668: 5665: 5662: 5659: 5655: 5651: 5646: 5643: 5640: 5637: 5633: 5622: 5605: 5585: 5582: 5579: 5553: 5550: 5521: 5518: 5489: 5460: 5438: 5437: 5421: 5415: 5412: 5408: 5404: 5401: 5396: 5393: 5389: 5385: 5381: 5374: 5370: 5365: 5358: 5354: 5350: 5346: 5342: 5339: 5337: 5327: 5324: 5321: 5318: 5315: 5312: 5308: 5304: 5303: 5299: 5293: 5290: 5280: 5277: 5272: 5269: 5259: 5255: 5248: 5244: 5239: 5234: 5224: 5221: 5219: 5209: 5206: 5203: 5200: 5197: 5194: 5190: 5186: 5185: 5180: 5170: 5167: 5162: 5152: 5149: 5147: 5137: 5134: 5131: 5128: 5125: 5121: 5117: 5116: 5112: 5106: 5103: 5093: 5090: 5085: 5082: 5072: 5068: 5061: 5057: 5052: 5047: 5037: 5034: 5032: 5022: 5019: 5016: 5013: 5010: 5007: 5003: 4999: 4998: 4975: 4955: 4935: 4915: 4912: 4909: 4889: 4869: 4849: 4838: 4837: 4822: 4818: 4813: 4808: 4804: 4800: 4795: 4791: 4787: 4784: 4781: 4778: 4772: 4765: 4762: 4758: 4750: 4747: 4740: 4737: 4734: 4730: 4726: 4716: 4713: 4710: 4707: 4704: 4701: 4697: 4673: 4669: 4665: 4662: 4657: 4654: 4650: 4646: 4639: 4636: 4633: 4629: 4625: 4620: 4617: 4614: 4611: 4608: 4604: 4592: 4591: 4574: 4571: 4566: 4559: 4556: 4552: 4544: 4541: 4538: 4534: 4530: 4528: 4518: 4515: 4512: 4509: 4506: 4503: 4499: 4495: 4494: 4489: 4486: 4481: 4474: 4471: 4467: 4459: 4456: 4453: 4449: 4445: 4443: 4433: 4430: 4427: 4424: 4421: 4418: 4414: 4410: 4409: 4382: 4378: 4374: 4369: 4365: 4361: 4356: 4352: 4346: 4343: 4323: 4319: 4315: 4312: 4309: 4306: 4303: 4300: 4297: 4292: 4289: 4285: 4281: 4274: 4271: 4268: 4264: 4260: 4257: 4252: 4249: 4244: 4240: 4234: 4231: 4228: 4224: 4220: 4215: 4212: 4209: 4206: 4203: 4200: 4196: 4164: 4161: 4158: 4155: 4152: 4149: 4145: 4121: 4101: 4081: 4059: 4056: 4053: 4050: 4047: 4044: 4040: 4036: 4031: 4028: 4018: 3998: 3973: 3970: 3967: 3964: 3961: 3958: 3955: 3952: 3949: 3946: 3943: 3940: 3937: 3934: 3914: 3892: 3889: 3886: 3883: 3880: 3876: 3852: 3832: 3812: 3786: 3781: 3777: 3754: 3751: 3747: 3726: 3723: 3720: 3717: 3714: 3709: 3706: 3702: 3698: 3695: 3692: 3687: 3684: 3680: 3676: 3673: 3670: 3667: 3664: 3661: 3658: 3655: 3645: 3642: 3639: 3636: 3633: 3629: 3608: 3605: 3602: 3597: 3594: 3590: 3569: 3566: 3563: 3560: 3557: 3552: 3547: 3543: 3539: 3536: 3533: 3528: 3525: 3521: 3517: 3514: 3511: 3508: 3505: 3502: 3499: 3496: 3491: 3488: 3485: 3482: 3479: 3475: 3450: 3445: 3442: 3439: 3431: 3428: 3421: 3417: 3413: 3409: 3406: 3403: 3400: 3396: 3390: 3386: 3382: 3379: 3376: 3373: 3367: 3363: 3359: 3355: 3352: 3349: 3346: 3343: 3339: 3334: 3327: 3323: 3318: 3317: 3314: 3311: 3308: 3300: 3295: 3291: 3287: 3283: 3280: 3277: 3274: 3270: 3266: 3265: 3262: 3259: 3256: 3248: 3245: 3238: 3234: 3230: 3226: 3223: 3220: 3217: 3213: 3207: 3203: 3199: 3196: 3193: 3190: 3184: 3180: 3176: 3172: 3169: 3166: 3163: 3160: 3156: 3151: 3144: 3140: 3135: 3134: 3132: 3127: 3122: 3117: 3114: 3111: 3103: 3100: 3094: 3090: 3086: 3082: 3079: 3076: 3073: 3069: 3065: 3054: 3050: 3046: 3043: 3040: 3035: 3030: 3029: 3026: 3023: 3020: 3012: 3007: 3003: 2999: 2995: 2992: 2989: 2986: 2982: 2978: 2977: 2974: 2971: 2968: 2960: 2957: 2951: 2947: 2943: 2939: 2936: 2933: 2930: 2926: 2922: 2911: 2907: 2903: 2900: 2897: 2892: 2887: 2886: 2884: 2879: 2869: 2866: 2863: 2860: 2857: 2853: 2825: 2822: 2819: 2816: 2813: 2809: 2788: 2768: 2748: 2726: 2723: 2720: 2717: 2714: 2710: 2675: 2646: 2623: 2620: 2589: 2531: 2504:given by spin 2486: 2483: 2480: 2460: 2457: 2454: 2434: 2414: 2394: 2374: 2361: 2360: 2357: 2354: 2351: 2348: 2345: 2342: 2338: 2337: 2334: 2331: 2328: 2325: 2322: 2319: 2310: 2309: 2306: 2304: 2301: 2298: 2295: 2292: 2283: 2282: 2279: 2277: 2275: 2272: 2269: 2266: 2257: 2256: 2253: 2251: 2249: 2247: 2244: 2241: 2232: 2231: 2228: 2226: 2224: 2222: 2220: 2209: 2206: 2201: 2197: 2186: 2177: 2176: 2173: 2165: 2157: 2149: 2141: 2133: 2114: 2110: 2086: 2083: 2078: 2074: 2070: 2067: 2064: 2042: 2038: 2017: 1987: 1983: 1947: 1944: 1941: 1921: 1918: 1915: 1888: 1885: 1882: 1855: 1852: 1847: 1843: 1839: 1836: 1833: 1830: 1813: 1755: 1752: 1737:Quantum number 1735:Main article: 1732: 1729: 1678:quantum states 1671:periodic table 1664: 1599:Main article: 1596: 1593: 1582:X-ray notation 1576:X-ray notation 1574:Main article: 1571: 1570:X-ray notation 1568: 1559: 1558: 1541: 1536: 1533: 1530: 1527: 1521: 1445: 1444: 1429: 1426: 1423: 1420: 1415: 1400: 1397: 1395: 1392: 1362:In chemistry, 1339: 1336: 1203: 1200: 1171: 1168: 1135:Main article: 1132: 1129: 1124: 1123: 1107: 1103: 1099: 1096: 1092: 1076: 1069: 1055: 1052: 1049: 1045: 1035:and decays as 981: 853: 850: 809: 794:quantum states 782:atomic physics 749:expansion and 741:of the atomic 733:of the atom's 731:electric field 718: 715: 692: 688: 667: 647: 605: 601: 580: 560: 536: 462:complex number 442: 441: 433: 426: 417: 416: 409: 398:standing waves 376: 373: 349:periodic table 254: 250: 212: 205: 190: 167:atom's nucleus 111:atomic orbital 56: 50: 44: 26: 18:Electron cloud 9: 6: 4: 3: 2: 13391: 13380: 13377: 13375: 13372: 13370: 13367: 13365: 13362: 13361: 13359: 13340: 13337: 13335: 13332: 13330: 13327: 13326: 13324: 13320: 13314: 13311: 13309: 13306: 13304: 13301: 13300: 13298: 13294: 13291: 13289: 13285: 13275: 13272: 13270: 13269:Covalent bond 13267: 13266: 13264: 13260: 13254: 13251: 13249: 13246: 13244: 13241: 13240: 13238: 13234: 13231: 13229: 13225: 13215: 13212: 13210: 13207: 13205: 13202: 13201: 13199: 13197: 13192: 13186: 13183: 13181: 13180:5 (quintuple) 13178: 13176: 13175:4 (quadruple) 13173: 13171: 13168: 13166: 13163: 13161: 13158: 13157: 13155: 13153: 13148: 13142: 13139: 13137: 13134: 13132: 13129: 13127: 13124: 13123: 13121: 13117: 13114: 13110: 13102: 13099: 13098: 13097: 13094: 13092: 13089: 13088: 13085: 13080: 13073: 13068: 13066: 13061: 13059: 13054: 13053: 13050: 13038: 13035: 13033: 13030: 13029: 13027: 13024: 13020: 13014: 13013:Core electron 13011: 13009: 13006: 13005: 13003: 12999: 12993: 12990: 12988: 12987:Electron pair 12985: 12984: 12982: 12978: 12972: 12969: 12967: 12964: 12962: 12959: 12958: 12956: 12952: 12946: 12943: 12941: 12938: 12937: 12935: 12931: 12925: 12918: 12916: 12909: 12907: 12900: 12898: 12891: 12890: 12888: 12886: 12882: 12874: 12871: 12870: 12869: 12866: 12864: 12861: 12859: 12856: 12855: 12852: 12848: 12841: 12836: 12834: 12829: 12827: 12822: 12821: 12818: 12806: 12802: 12798: 12794: 12792: 12784: 12783: 12780: 12773: 12769: 12767: 12763: 12762: 12760: 12756: 12749: 12745: 12742: 12738: 12736: 12732: 12729: 12728:Nagaoka model 12725: 12722: 12718: 12715: 12711: 12708: 12704: 12703: 12701: 12697: 12693: 12692:Atomic models 12686: 12681: 12679: 12674: 12672: 12667: 12666: 12663: 12656: 12653: 12650: 12647: 12645: 12642: 12641: 12631: 12627: 12623: 12619: 12615: 12611: 12610:J. Chem. Educ 12606: 12602: 12596: 12592: 12587: 12583: 12577: 12573: 12568: 12564: 12558: 12553: 12552: 12545: 12541: 12535: 12531: 12526: 12522: 12520:9781783264162 12516: 12512: 12511: 12505: 12504: 12497: 12485: 12470: 12464: 12460: 12456: 12452: 12448: 12447: 12439: 12431: 12427: 12423: 12419: 12415: 12411: 12404: 12396: 12392: 12387: 12382: 12378: 12374: 12370: 12366: 12362: 12355: 12347: 12340: 12332: 12328: 12324: 12320: 12316: 12312: 12308: 12304: 12303: 12298: 12292: 12284: 12278: 12270: 12266: 12262: 12258: 12254: 12250: 12246: 12242: 12235: 12227: 12223: 12219: 12215: 12211: 12207: 12200: 12192: 12188: 12184: 12180: 12176: 12172: 12165: 12156: 12151: 12147: 12143: 12139: 12135: 12131: 12124: 12122: 12113: 12112: 12104: 12096: 12092: 12088: 12084: 12080: 12076: 12075:J. Chem. Educ 12069: 12061: 12055: 12051: 12045: 12037: 12033: 12029: 12025: 12018: 12010: 12004: 12000: 11993: 11985: 11979: 11975: 11968: 11960: 11954: 11950: 11943: 11935: 11929: 11925: 11918: 11910: 11904: 11900: 11893: 11885: 11881: 11877: 11873: 11869: 11865: 11861: 11857: 11856: 11848: 11840: 11834: 11830: 11829: 11821: 11812: 11807: 11803: 11799: 11795: 11791: 11787: 11780: 11772: 11768: 11764: 11760: 11756: 11752: 11748: 11744: 11743: 11735: 11719: 11715: 11711: 11707: 11703: 11699: 11692: 11684: 11678: 11674: 11673: 11665: 11657: 11653: 11649: 11645: 11644: 11636: 11629: 11621: 11617: 11613: 11609: 11605: 11598: 11590: 11584: 11580: 11575: 11574: 11565: 11549: 11545: 11541: 11537: 11533: 11529: 11522: 11520: 11511: 11507: 11503: 11499: 11495: 11491: 11487: 11483: 11479: 11472: 11470: 11461: 11457: 11453: 11449: 11445: 11441: 11440: 11432: 11425: 11421: 11419:0-205-12770-3 11415: 11411: 11404: 11398: 11397: 11392: 11391:Roger Penrose 11387: 11379: 11373: 11369: 11362: 11354: 11348: 11344: 11343: 11335: 11327: 11321: 11317: 11310: 11302: 11296: 11292: 11288: 11287: 11279: 11271: 11265: 11261: 11254: 11246: 11240: 11236: 11235: 11227: 11216: 11212: 11205: 11198: 11194: 11184: 11181: 11179: 11176: 11174: 11171: 11169: 11166: 11164: 11161: 11159: 11156: 11154: 11151: 11149: 11146: 11144: 11141: 11139: 11136: 11134: 11131: 11130: 11123: 11119: 11116: 11109: 11102: 11093: 11086: 11077: 11068: 11043: 11032: 11028: 11021: 11014: 11009: 10990: 10979: 10975: 10968: 10961: 10956: 10955: 10954: 10951: 10946: 10936: 10934: 10930: 10926: 10914: 10910: 10906: 10894: 10890: 10880: 10877: 10858: 10854: 10850: 10846: 10830: 10827: 10824: 10816: 10810: 10805: 10789: 10765: 10762: 10759: 10756: 10753: 10743: 10738: 10733: 10731: 10727: 10722: 10709: 10703: 10693: 10691: 10690: 10685: 10684:atomic number 10680: 10678: 10667: 10664: 10661: 10658: 10655: 10652: 10649: 10646: 10643: 10640: 10637: 10634: 10631: 10628: 10625: 10622: 10621: 10617: 10614: 10611: 10608: 10605: 10602: 10599: 10596: 10593: 10590: 10587: 10584: 10581: 10578: 10575: 10572: 10571: 10567: 10564: 10561: 10558: 10555: 10552: 10549: 10546: 10544: 10542: 10540: 10538: 10536: 10534: 10532: 10529: 10528: 10524: 10521: 10518: 10515: 10512: 10509: 10506: 10503: 10501: 10499: 10497: 10495: 10493: 10491: 10489: 10486: 10485: 10481: 10478: 10475: 10473: 10471: 10469: 10467: 10465: 10463: 10461: 10459: 10457: 10455: 10453: 10451: 10448: 10447: 10443: 10440: 10437: 10435: 10433: 10431: 10429: 10427: 10425: 10423: 10421: 10419: 10417: 10415: 10413: 10410: 10409: 10406: 10404: 10402: 10400: 10398: 10396: 10394: 10392: 10390: 10388: 10386: 10384: 10382: 10380: 10378: 10375: 10374: 10371: 10369: 10365: 10361: 10357: 10350: 10347: 10346: 10345: 10342: 10340: 10336: 10332: 10328: 10312: 10307: 10305: 10301: 10297: 10293: 10289: 10284: 10282: 10276: 10222: 10218: 10214: 10213: 10206: 10202: 10178: 10170: 10169:Madelung rule 10166: 10162: 10157: 10148: 10147: 10139: 10136: 10134: 10131: 10129: 10126: 10124: 10121: 10119: 10116: 10114: 10111: 10109: 10106: 10105: 10102: 10099: 10097: 10094: 10092: 10089: 10087: 10084: 10082: 10079: 10077: 10074: 10072: 10069: 10068: 10065: 10062: 10060: 10057: 10055: 10052: 10050: 10047: 10045: 10042: 10040: 10037: 10035: 10032: 10031: 10028: 10025: 10023: 10020: 10018: 10015: 10013: 10010: 10007: 10004: 10002: 9999: 9998: 9995: 9992: 9990: 9987: 9985: 9982: 9979: 9976: 9973: 9971: 9968: 9967: 9964: 9962: 9959: 9956: 9953: 9950: 9947: 9945: 9942: 9941: 9938: 9936: 9933: 9930: 9927: 9924: 9922: 9919: 9918: 9915: 9913: 9911: 9908: 9905: 9902: 9900: 9897: 9896: 9893: 9891: 9889: 9887: 9884: 9881: 9879: 9876: 9875: 9872: 9870: 9868: 9866: 9864: 9861: 9859: 9856: 9855: 9851: 9848: 9845: 9842: 9839: 9836: 9833: 9828: 9824: 9823: 9820: 9805: 9785: 9776: 9762: 9742: 9732: 9718: 9715: 9712: 9692: 9689: 9686: 9666: 9646: 9626: 9618: 9617:energy levels 9612: 9610: 9606: 9602: 9578: 9558: 9538: 9518: 9498: 9478: 9475: 9472: 9452: 9444: 9438: 9411: 9407: 9395: 9390: 9373: 9369: 9357: 9352: 9335: 9331: 9319: 9314: 9311: 9310: 9291: 9287: 9283: 9280: 9263: 9251: 9246: 9228: 9224: 9220: 9217: 9200: 9188: 9183: 9165: 9161: 9157: 9154: 9137: 9125: 9120: 9103: 9099: 9087: 9082: 9065: 9061: 9049: 9044: 9027: 9023: 9011: 9006: 9003: 9002: 9001: 8998: 8994: 8990: 8986: 8981: 8978: 8955: 8951: 8947: 8944: 8927: 8915: 8910: 8892: 8888: 8884: 8881: 8864: 8852: 8847: 8829: 8825: 8821: 8818: 8801: 8789: 8784: 8767: 8763: 8751: 8746: 8729: 8725: 8713: 8708: 8691: 8687: 8675: 8670: 8667: 8666: 8665: 8661: 8657: 8653: 8645: 8641: 8633: 8631: 8627: 8623: 8619: 8615: 8610: 8608: 8604: 8600: 8595: 8593: 8589: 8575: 8571: 8569: 8553: 8550: 8547: 8544: 8541: 8538: 8535: 8532: 8529: 8507: 8497: 8473: 8470: 8467: 8458: 8456: 8452: 8448: 8444: 8440: 8435: 8434: 8432: 8428: 8421: 8420: 8410: 8407: 8404: 8401: 8398: 8395: 8392: 8389: 8386: 8383: 8380: 8377: 8374: 8371: 8368: 8365: 8362: 8359: 8356: 8353: 8350: 8347: 8344: 8341: 8338: 8335: 8332: 8329: 8326: 8323: 8320: 8316: 8312: 8308: 8307: 8303: 8300: 8297: 8294: 8291: 8288: 8285: 8282: 8279: 8276: 8273: 8270: 8267: 8264: 8261: 8258: 8255: 8252: 8249: 8246: 8243: 8240: 8237: 8234: 8231: 8227: 8224: 8220: 8217: 8213: 8210: 8206: 8202: 8198: 8197: 8194: 8191: 8189: 8186: 8184: 8181: 8179: 8176: 8174: 8171: 8169: 8166: 8164: 8161: 8158: 8154: 8151: 8147: 8144: 8140: 8137: 8133: 8130: 8126: 8123: 8119: 8116: 8112: 8109: 8105: 8102: 8098: 8094: 8090: 8089: 8085: 8081: 8078: 8074: 8071: 8067: 8064: 8060: 8057: 8053: 8050: 8046: 8043: 8039: 8036: 8032: 8029: 8025: 8022: 8018: 8015: 8011: 8008: 8004: 8001: 7997: 7994: 7990: 7987: 7983: 7980: 7976: 7972: 7968: 7967: 7964: 7962: 7960: 7958: 7956: 7954: 7952: 7949: 7945: 7942: 7938: 7935: 7931: 7928: 7924: 7921: 7917: 7914: 7910: 7907: 7903: 7900: 7896: 7893: 7889: 7885: 7881: 7880: 7877: 7875: 7873: 7871: 7869: 7867: 7865: 7863: 7861: 7859: 7857: 7855: 7852: 7848: 7845: 7841: 7838: 7834: 7831: 7827: 7823: 7819: 7818: 7815: 7813: 7811: 7809: 7807: 7805: 7803: 7801: 7799: 7797: 7795: 7793: 7791: 7789: 7787: 7784: 7780: 7776: 7772: 7771: 7766: 7762: 7758: 7753: 7749: 7745: 7741: 7736: 7732: 7728: 7724: 7719: 7716: 7711: 7708: 7703: 7700: 7695: 7692: 7687: 7684: 7680: 7675: 7672: 7667: 7664: 7659: 7656: 7651: 7648: 7643: 7640: 7635: 7632: 7627: 7624: 7619: 7616: 7614: 7613: 7608: 7600: 7592: 7584: 7580: 7576: 7568: 7560: 7556: 7552: 7544: 7540: 7536: 7532: 7530: 7529: 7523: 7513: 7503: 7493: 7488: 7486: 7485: 7482: 7480: 7453: 7432: 7423: 7407: 7400: 7399:wave function 7397: 7393: 7389: 7379: 7377: 7361: 7352: 7348: 7344: 7334: 7328: 7321: 7317: 7312: 7296: 7293: 7291: 7284: 7278: 7269: 7265: 7261: 7257: 7253: 7247: 7242: 7237: 7230: 7219: 7214: 7208: 7191: 7188: 7185: 7176: 7159: 7138: 7134: 7119: 7113: 7087: 7080: 7059: 7058:nodal spheres 7055: 7053: 7048: 7044: 7039: 7033: 7026: 7022: 7014: 7010: 6995: 6986: 6982: 6979: 6978:standing wave 6974: 6970: 6966: 6962: 6954: 6950: 6946: 6936: 6932: 6928: 6920: 6914: 6910: 6906: 6898: 6894: 6890: 6879: 6875: 6871: 6867: 6862: 6861:wave function 6858: 6852: 6844: 6840: 6836: 6830: 6819: 6812: 6808: 6804: 6797: 6765: 6761: 6757: 6754: 6749: 6745: 6738: 6724: 6703: 6699: 6695: 6690: 6686: 6679: 6665: 6647: 6643: 6639: 6625: 6607: 6603: 6588: 6570: 6566: 6562: 6548: 6532: 6529: 6526: 6512: 6491: 6487: 6483: 6478: 6474: 6470: 6464: 6450: 6436: 6433: 6430: 6423: 6422: 6419: 6401: 6397: 6393: 6388: 6384: 6369: 6353: 6350: 6336: 6318: 6314: 6299: 6283: 6280: 6266: 6250: 6247: 6233: 6231: 6217: 6214: 6211: 6204: 6203: 6200: 6198: 6182: 6168: 6152: 6138: 6122: 6108: 6106: 6104: 6090: 6087: 6084: 6077: 6076: 6073: 6071: 6069: 6046: 6044: 6042: 6040: 6026: 6023: 6020: 6013: 6012: 5995: 5992: 5989: 5986: 5982: 5978: 5973: 5970: 5967: 5964: 5960: 5952: 5936: 5933: 5930: 5927: 5923: 5919: 5914: 5911: 5908: 5905: 5901: 5893: 5877: 5874: 5871: 5868: 5864: 5860: 5855: 5852: 5849: 5846: 5842: 5834: 5818: 5815: 5812: 5808: 5800: 5784: 5781: 5778: 5775: 5771: 5767: 5762: 5759: 5756: 5753: 5749: 5741: 5725: 5722: 5719: 5716: 5712: 5708: 5703: 5700: 5697: 5694: 5690: 5682: 5666: 5663: 5660: 5657: 5653: 5649: 5644: 5641: 5638: 5635: 5631: 5623: 5621: 5620: 5617: 5603: 5583: 5580: 5577: 5567: 5551: 5548: 5519: 5516: 5487: 5458: 5443: 5419: 5413: 5410: 5406: 5402: 5399: 5394: 5391: 5387: 5383: 5379: 5372: 5368: 5363: 5356: 5352: 5348: 5344: 5340: 5335: 5325: 5322: 5319: 5316: 5313: 5310: 5306: 5297: 5291: 5288: 5278: 5275: 5270: 5267: 5257: 5253: 5246: 5242: 5237: 5232: 5222: 5217: 5207: 5204: 5201: 5198: 5195: 5192: 5188: 5178: 5168: 5165: 5160: 5150: 5145: 5135: 5132: 5129: 5126: 5123: 5119: 5110: 5104: 5101: 5091: 5088: 5083: 5080: 5070: 5066: 5059: 5055: 5050: 5045: 5035: 5030: 5020: 5017: 5014: 5011: 5008: 5005: 5001: 4989: 4988: 4987: 4973: 4953: 4933: 4913: 4910: 4907: 4887: 4867: 4847: 4820: 4816: 4806: 4802: 4798: 4793: 4789: 4785: 4779: 4776: 4770: 4763: 4760: 4756: 4748: 4745: 4738: 4735: 4732: 4728: 4724: 4714: 4711: 4708: 4705: 4702: 4699: 4695: 4687: 4686: 4685: 4671: 4667: 4663: 4660: 4655: 4652: 4648: 4644: 4637: 4634: 4631: 4627: 4623: 4618: 4615: 4612: 4609: 4606: 4602: 4572: 4569: 4564: 4557: 4554: 4550: 4542: 4539: 4536: 4532: 4526: 4516: 4513: 4510: 4507: 4504: 4501: 4497: 4487: 4484: 4479: 4472: 4469: 4465: 4457: 4454: 4451: 4447: 4441: 4431: 4428: 4425: 4422: 4419: 4416: 4412: 4400: 4399: 4398: 4380: 4376: 4372: 4367: 4363: 4359: 4354: 4350: 4344: 4341: 4321: 4317: 4310: 4307: 4304: 4301: 4295: 4290: 4287: 4283: 4279: 4272: 4269: 4266: 4262: 4258: 4255: 4250: 4247: 4242: 4238: 4232: 4229: 4226: 4222: 4218: 4213: 4210: 4207: 4204: 4201: 4198: 4194: 4185: 4162: 4159: 4156: 4153: 4150: 4147: 4143: 4133: 4119: 4099: 4079: 4057: 4054: 4051: 4048: 4045: 4042: 4038: 4034: 4029: 4026: 4016: 3996: 3971: 3968: 3965: 3962: 3959: 3956: 3953: 3950: 3947: 3944: 3941: 3938: 3935: 3932: 3912: 3890: 3887: 3884: 3881: 3878: 3874: 3864: 3850: 3830: 3810: 3800: 3784: 3779: 3775: 3752: 3749: 3745: 3721: 3718: 3715: 3707: 3704: 3700: 3693: 3685: 3682: 3678: 3674: 3668: 3665: 3662: 3659: 3656: 3643: 3640: 3637: 3634: 3631: 3627: 3603: 3595: 3592: 3588: 3564: 3561: 3558: 3550: 3545: 3541: 3534: 3526: 3523: 3519: 3515: 3509: 3506: 3503: 3500: 3497: 3489: 3486: 3483: 3480: 3477: 3473: 3463: 3443: 3440: 3437: 3426: 3415: 3407: 3404: 3401: 3398: 3394: 3388: 3380: 3377: 3371: 3361: 3353: 3350: 3347: 3344: 3341: 3337: 3332: 3325: 3321: 3312: 3309: 3306: 3289: 3281: 3278: 3275: 3272: 3268: 3260: 3257: 3254: 3243: 3232: 3224: 3221: 3218: 3215: 3211: 3205: 3197: 3194: 3188: 3178: 3170: 3167: 3164: 3161: 3158: 3154: 3149: 3142: 3138: 3130: 3125: 3115: 3112: 3109: 3098: 3088: 3080: 3077: 3074: 3071: 3067: 3063: 3052: 3044: 3041: 3033: 3024: 3021: 3018: 3001: 2993: 2990: 2987: 2984: 2980: 2972: 2969: 2966: 2955: 2945: 2937: 2934: 2931: 2928: 2924: 2920: 2909: 2901: 2898: 2890: 2882: 2877: 2867: 2864: 2861: 2858: 2855: 2851: 2823: 2820: 2817: 2814: 2811: 2807: 2786: 2766: 2746: 2724: 2721: 2718: 2715: 2712: 2708: 2699: 2695: 2673: 2644: 2628: 2622:Real orbitals 2619: 2617: 2611: 2604: 2599: 2594: 2592: 2573: 2568: 2534: 2527: 2507: 2503: 2498: 2484: 2481: 2478: 2458: 2455: 2452: 2432: 2412: 2392: 2372: 2358: 2355: 2352: 2349: 2346: 2343: 2340: 2339: 2335: 2332: 2329: 2326: 2323: 2320: 2316: 2312: 2311: 2307: 2305: 2302: 2299: 2296: 2293: 2289: 2285: 2284: 2280: 2278: 2276: 2273: 2270: 2267: 2263: 2259: 2258: 2254: 2252: 2250: 2248: 2245: 2242: 2238: 2234: 2233: 2229: 2227: 2225: 2223: 2221: 2207: 2204: 2199: 2195: 2187: 2183: 2179: 2178: 2174: 2170: 2166: 2162: 2158: 2154: 2150: 2146: 2142: 2138: 2134: 2132: 2131: 2128: 2112: 2108: 2098: 2084: 2081: 2076: 2072: 2068: 2065: 2062: 2040: 2036: 2015: 2007: 2006:Ampèrian loop 2003: 1985: 1981: 1972: 1967: 1965: 1945: 1942: 1939: 1919: 1916: 1913: 1903: 1886: 1883: 1880: 1870: 1853: 1850: 1845: 1841: 1837: 1834: 1831: 1828: 1812: 1800: 1795: 1793: 1792: 1787: 1783: 1776: 1771: 1769: 1760: 1751: 1749: 1745: 1738: 1728: 1726: 1718: 1714: 1710: 1706: 1698: 1689: 1687: 1683: 1679: 1674: 1672: 1667: 1658: 1652: 1646: 1644: 1643:qualitatively 1639: 1637: 1636:hydrogen atom 1633: 1629: 1625: 1621: 1617: 1612: 1608: 1607:hydrogen atom 1602: 1592: 1588: 1583: 1577: 1567: 1539: 1519: 1512: 1511: 1510: 1508: 1499: 1495: 1488: 1481: 1475: 1469: 1465: 1461: 1454: 1450: 1413: 1406: 1405: 1404: 1394:Orbital names 1391: 1389: 1385: 1380: 1377: 1373: 1369: 1368:Linus Pauling 1365: 1360: 1357: 1353: 1349: 1345: 1335: 1333: 1329: 1325: 1321: 1317: 1313: 1309: 1305: 1301: 1297: 1293: 1289: 1284: 1282: 1279:treatment of 1278: 1274: 1269: 1267: 1262: 1258: 1253: 1249: 1245: 1241: 1233: 1228: 1224: 1222: 1218: 1214: 1209: 1199: 1197: 1192: 1187: 1185: 1181: 1177: 1176:J. J. Thomson 1167: 1165: 1160: 1156: 1152: 1148: 1144: 1138: 1137:Atomic theory 1128: 1105: 1101: 1097: 1094: 1090: 1081: 1077: 1074: 1070: 1053: 1050: 1047: 1043: 1034: 1030: 1026: 1022: 1018: 1017: 1016: 1012: 1008: 993: 989: 984: 980: 976: 972: 966: 962: 954: 950: 946: 942: 938: 934: 930: 926: 919: 915: 911: 906: 903:in atoms and 900: 896: 892: 887: 883: 879: 875: 867: 863: 862:hydrogen-like 858: 849: 847: 843: 837: 835: 830: 827:ruled by the 826: 822: 818: 813: 807: 803: 799: 795: 791: 790:quantum leaps 787: 783: 778: 776: 772: 768: 764: 760: 756: 752: 748: 744: 740: 736: 732: 728: 724: 714: 712: 711:Real orbitals 708: 690: 686: 665: 645: 637: 603: 599: 578: 558: 550: 534: 463: 459: 455: 450: 448: 439: 438:superposition 434: 431: 427: 424: 423: 422: 421: 414: 413:wave function 410: 407: 403: 399: 395: 394: 393: 392: 388: 386: 382: 368: 364: 362: 358: 350: 346: 342: 338: 337:hydrogen-like 334: 329: 325: 320: 316: 312: 308: 304: 301: 297: 287: 282: 278: 274: 270: 252: 248: 240: 235: 232: 228: 223: 219: 201: 197: 179: 174: 172: 168: 164: 160: 156: 152: 148: 142: 112: 108: 100: 94: 90: 86: 78: 74: 70: 64: 59: 53: 47: 41: 37: 33: 19: 13185:6 (sextuple) 13152:multiplicity 13090: 12862: 12765: 12716:(knot model) 12707:Dalton model 12649:The Orbitron 12613: 12609: 12590: 12571: 12550: 12529: 12509: 12472:. Retrieved 12445: 12438: 12413: 12409: 12403: 12368: 12364: 12354: 12339: 12306: 12300: 12291: 12277:cite journal 12244: 12240: 12234: 12209: 12205: 12199: 12174: 12170: 12164: 12137: 12133: 12110: 12103: 12078: 12074: 12068: 12049: 12044: 12027: 12023: 12017: 11998: 11992: 11973: 11967: 11948: 11942: 11923: 11917: 11898: 11892: 11859: 11853: 11847: 11827: 11820: 11793: 11789: 11779: 11746: 11740: 11734: 11722:. Retrieved 11718:the original 11705: 11701: 11691: 11671: 11664: 11647: 11646:. Series 6. 11641: 11628: 11614:(269): 293. 11611: 11607: 11597: 11572: 11564: 11552:. Retrieved 11548:the original 11535: 11531: 11485: 11481: 11446:(1): 49–71. 11443: 11437: 11431: 11423: 11409: 11403: 11394: 11386: 11367: 11361: 11341: 11334: 11315: 11309: 11285: 11278: 11259: 11253: 11233: 11226: 11210: 11197: 11158:Hund's rules 11153:Energy level 11120: 11117: 11107: 11100: 11091: 11084: 11075: 11066: 11063: 11038: 11030: 11026: 11019: 11012: 10985: 10977: 10973: 10966: 10959: 10952: 10948: 10886: 10878: 10849:untriseptium 10808: 10741: 10734: 10723: 10711: 10687: 10681: 10673: 10367: 10363: 10359: 10355: 10353: 10348: 10343: 10308: 10295: 10291: 10285: 10277: 10210: 10208: 10172: 10164: 10145: 10144: 10137: 10132: 10127: 10122: 10117: 10112: 10107: 10100: 10095: 10090: 10085: 10080: 10075: 10070: 10063: 10058: 10053: 10048: 10043: 10038: 10033: 10026: 10021: 10016: 10011: 10000: 9993: 9988: 9983: 9969: 9960: 9943: 9920: 9898: 9877: 9857: 9831: 9826: 9777: 9733: 9639:but also on 9613: 9604: 9440: 8996: 8992: 8988: 8984: 8982: 8976: 8974: 8659: 8655: 8651: 8643: 8639: 8634: 8613: 8611: 8606: 8598: 8596: 8585: 8459: 8438: 8436: 8424: 8422: 8418: 8416: 8408: 8402: 8396: 8390: 8384: 8378: 8372: 8366: 8360: 8354: 8348: 8342: 8336: 8330: 8324: 8310: 8301: 8295: 8289: 8283: 8277: 8271: 8265: 8259: 8253: 8247: 8241: 8235: 8200: 8192: 8187: 8182: 8177: 8172: 8167: 8162: 8092: 7970: 7883: 7821: 7774: 7764: 7760: 7756: 7747: 7743: 7739: 7730: 7726: 7722: 7714: 7706: 7698: 7690: 7682: 7678: 7670: 7662: 7654: 7646: 7638: 7630: 7622: 7606: 7598: 7590: 7582: 7574: 7566: 7558: 7550: 7542: 7534: 7521: 7511: 7501: 7491: 7451: 7430: 7421: 7405: 7395: 7391: 7385: 7357: 7342: 7332: 7326: 7313: 7297: 7294: 7282: 7279: 7245: 7240: 7238: 7228: 7217: 7206: 7177: 7144: 7121:In general, 7120: 7112:eccentricity 7085: 7078: 7057: 7050: 7049: 7042: 7037: 7031: 7024: 7020: 7012: 7008: 6993: 6981:interference 6975: 6968: 6964: 6960: 6952: 6948: 6944: 6934: 6930: 6926: 6912: 6908: 6904: 6896: 6892: 6888: 6880: 6873: 6869: 6865: 6850: 6842: 6838: 6834: 6825: 6817: 6810: 6806: 6802: 5568: 5439: 4839: 4593: 4134: 3865: 3801: 3464: 2693: 2691: 2609: 2602: 2597: 2595: 2587: 2569: 2529: 2505: 2499: 2364: 2314: 2287: 2261: 2236: 2181: 2168: 2160: 2152: 2144: 2136: 2099: 1968: 1963: 1901: 1868: 1810: 1796: 1789: 1785: 1772: 1765: 1740: 1716: 1708: 1704: 1690: 1675: 1647: 1642: 1640: 1626:series, and 1604: 1586: 1579: 1560: 1506: 1505:is called a 1500: 1496:= 1, 2 and 3 1493: 1486: 1479: 1476: 1459: 1448: 1446: 1402: 1387: 1383: 1381: 1361: 1341: 1331: 1327: 1323: 1319: 1315: 1291: 1285: 1270: 1261:matter waves 1256: 1237: 1205: 1188: 1173: 1170:Early models 1146: 1140: 1125: 1028: 1020: 1010: 1006: 991: 987: 982: 978: 964: 960: 952: 948: 944: 940: 936: 932: 928: 924: 917: 913: 909: 898: 894: 890: 871: 865: 842:Hartree–Fock 838: 814: 779: 766: 720: 512:(2, 1, 0) + 480:(2, 1, 0) + 451: 443: 419: 418: 390: 389: 378: 340: 332: 330: 323: 300:alkali metal 285: 280: 276: 272: 268: 236: 230: 226: 221: 175: 110: 104: 92: 88: 84: 76: 72: 68: 57: 51: 45: 36: 13119:By symmetry 12966:Hund's rule 12721:Lewis model 12655:Grand table 12416:(10): 678. 12297:Bohr, Niels 11708:(41): 446. 10304:periodicity 7106:is energy, 4182:. From the 3984:are called 1628:exponential 1616:eigenstates 1509:, denoted 1356:wave packet 1314:. Thus the 802:term symbol 743:Hamiltonian 636:eigenstates 460:, but with 454:eigenstates 341:periodicity 319:fundamental 171:probability 165:around the 13358:Categories 13329:Bonding MO 13313:MO diagram 13170:3 (triple) 13165:2 (double) 13160:1 (single) 13032:Octet rule 12748:Bohr model 12616:(4): 187. 12309:(1): 117. 12212:(2): 188. 12081:(7): 354. 11488:(1): 476. 11190:References 10857:feynmanium 10737:Bohr model 10706:See also: 10300:Niels Bohr 10298:th shell. 10236:. Because 9609:Lamb shift 9399:Drum mode 9361:Drum mode 9323:Drum mode 9091:Drum mode 9053:Drum mode 9015:Drum mode 8755:Drum mode 8717:Drum mode 8679:Drum mode 7252:ellipsoids 7213:solid ball 1899:, and the 1697:Bohr model 1624:polynomial 1344:Heisenberg 1273:de Broglie 1221:Bohr model 1213:Niels Bohr 1151:Niels Bohr 836:is large. 821:transition 792:) between 739:eigenstate 549:eigenvalue 288:= 0, 1, 2, 13274:Lone pair 13248:Resonance 13136:Delta (δ) 13126:Sigma (σ) 12805:Chemistry 12494:ignored ( 12484:cite book 12474:4 October 12331:123582460 12269:120472894 12177:(1): 45. 11884:126109346 11771:122763326 10845:unbounded 10790:α 10763:α 10161:molecular 9806:ℓ 9743:ℓ 9713:ℓ 9687:ℓ 9667:ℓ 9647:ℓ 9559:ℓ 8626:particles 8620:with the 8554:⋯ 8545:± 8536:± 8501:^ 7186:ℓ 6755:− 6696:− 6484:− 6431:ℓ 6394:− 6212:ℓ 6085:ℓ 6021:ℓ 5983:ψ 5979:− 5971:− 5961:ψ 5924:ψ 5920:− 5912:− 5902:ψ 5865:ψ 5861:− 5853:− 5843:ψ 5809:ψ 5772:ψ 5760:− 5750:ψ 5713:ψ 5701:− 5691:ψ 5654:ψ 5642:− 5632:ψ 5578:ℓ 5549:− 5400:− 5392:− 5307:ψ 5276:− 5268:− 5189:ψ 5120:ψ 5081:− 5018:− 5002:ψ 4974:ℓ 4799:− 4780:⋅ 4771:⋅ 4764:π 4696:ψ 4661:⋅ 4656:π 4603:ψ 4594:Likewise 4565:⋅ 4558:π 4514:− 4498:ψ 4480:⋅ 4473:π 4413:ψ 4305:± 4296:⋅ 4291:π 4259:∓ 4248:± 4211:± 4195:ψ 4160:± 4144:ψ 4100:ℓ 4055:± 4039:ψ 4027:± 3997:… 3972:… 3925:equal to 3913:ℓ 3885:ℓ 3875:ψ 3831:ℓ 3780:ℓ 3750:ℓ 3722:ϕ 3716:θ 3705:ℓ 3669:ϕ 3663:θ 3638:ℓ 3628:ψ 3565:ϕ 3559:θ 3546:ℓ 3510:ϕ 3504:θ 3484:ℓ 3474:ψ 3405:ℓ 3395:ψ 3378:− 3354:− 3348:ℓ 3338:ψ 3279:ℓ 3269:ψ 3222:ℓ 3212:ψ 3195:− 3189:− 3171:− 3165:ℓ 3155:ψ 3078:ℓ 3068:ψ 3042:− 2991:ℓ 2981:ψ 2935:ℓ 2925:ψ 2899:− 2862:ℓ 2852:ψ 2818:ℓ 2808:ψ 2719:ℓ 2709:ψ 2479:ℓ 2433:ℓ 2405:-values. 2393:ℓ 2246:−1, 0, 1 2200:ℓ 2113:ℓ 2085:ℓ 2082:≤ 2077:ℓ 2069:≤ 2066:ℓ 2063:− 2041:ℓ 2016:ℓ 1986:ℓ 1940:ℓ 1914:ℓ 1881:ℓ 1851:− 1838:≤ 1835:ℓ 1832:≤ 1206:In 1909, 1202:Bohr atom 1098:α 1095:− 1051:α 1048:− 905:Cartesian 751:basis set 406:harmonics 311:principal 281:f orbital 277:d orbital 273:p orbital 269:s orbital 13296:Concepts 13236:Concepts 12395:25666072 11215:Archived 11126:See also 10931:through 10887:In late 10778:, where 8603:antinode 7264:dumbbell 6973:graphs. 2659:and the 2324:−1, 0, 1 2297:−1, 0, 1 2271:−1, 0, 1 2004:via the 1964:subshell 1725:subshell 1507:subshell 1464:subshell 1388:n-sphere 1372:Max Born 1288:hydrogen 1248:emission 1240:Einstein 825:fermions 713:below). 345:elements 155:electron 147:function 55:, and 2p 13209:Singlet 13204:Triplet 13141:Phi (φ) 12618:Bibcode 12418:Bibcode 12373:Bibcode 12311:Bibcode 12249:Bibcode 12214:Bibcode 12179:Bibcode 12142:Bibcode 12083:Bibcode 11864:Bibcode 11798:Bibcode 11751:Bibcode 11510:3977652 11490:Bibcode 11448:Bibcode 11291:144–145 11058:⁠ 11046:⁠ 11005:⁠ 10993:⁠ 10909:p-block 10802:is the 10735:In the 10730:caesium 10726:mercury 10273:⁠ 10261:⁠ 10257:⁠ 10245:⁠ 8605:in all 7260:nucleus 7258:at the 7254:with a 7141:(STEM). 7096:ℓ ≤ n-1 4397:. Then 3580:, with 2565:⁠ 2553:⁠ 2549:⁠ 2537:⁠ 2522:⁠ 2510:⁠ 2171:= 4 (g) 2163:= 3 (f) 2155:= 2 (d) 2147:= 1 (p) 2139:= 0 (s) 1748:complex 1634:. (see 1618:of the 1611:ionized 1131:History 996:(where 753:) into 735:nucleus 632:⁠ 620:⁠ 526:⁠ 514:⁠ 510:⁠ 498:⁠ 494:⁠ 482:⁠ 478:⁠ 466:⁠ 315:diffuse 220:(e.g., 145:) is a 13131:Pi (π) 13081:theory 12597: 12578: 12559: 12536: 12517: 12465: 12451:89–144 12393: 12329: 12267: 12056: 12005: 11980: 11955: 11930: 11905: 11882: 11835: 11790:Nature 11769: 11724:30 May 11679: 11585: 11581:–143. 11554:30 May 11508: 11416: 11374: 11349: 11322: 11297: 11266: 11241: 11010:State 10957:State 10929:indium 10919:and 9p 10899:and 9p 10893:hybrid 10806:, and 10366:, and 10311:blocks 10281:photon 9465:. The 7388:radium 7114:, and 7054:planes 7023:⟩ − ⟨− 7011:⟩ + ⟨− 6939:| 6923:| 6820:> 1 4880:, and 3737:where 2779:, and 2385:- and 1932:, and 1660:, and 1545: 1470: 1447:where 1432: 1296:helium 876:for a 784:, the 678:, but 430:photon 326:> 3 317:, and 279:, and 187:, and 157:in an 153:of an 13025:rules 12770:1928 12764:1926 12746:1913 12739:1911 12733:1904 12726:1904 12719:1902 12712:1867 12705:1804 12327:S2CID 12265:S2CID 11880:S2CID 11767:S2CID 11506:S2CID 11218:(PDF) 11207:(PDF) 10933:xenon 10895:of 8p 10739:, an 8630:limit 8409:. . . 8403:. . . 8397:. . . 8391:. . . 8385:. . . 8379:. . . 8373:. . . 8367:. . . 8361:. . . 8355:. . . 8349:. . . 8343:. . . 8337:. . . 8331:. . . 8325:. . . 8302:. . . 8296:. . . 8290:. . . 8284:. . . 8278:. . . 8272:. . . 8266:. . . 8260:. . . 8254:. . . 8248:. . . 8242:. . . 8236:. . . 8193:. . . 8188:. . . 8183:. . . 8178:. . . 8173:. . . 8168:. . . 8163:. . . 7290:torus 7268:shell 7092:n-ℓ-1 7052:Nodal 7029:. If 6917:is a 6809:= 0, 6805:= 6, 4334:with 2607:from 1713:shell 1566:= 1. 1300:argon 1271:With 1174:With 1033:nodes 707:basis 357:order 307:sharp 109:, an 65:of a 13308:LCAO 13196:spin 12595:ISBN 12576:ISBN 12557:ISBN 12534:ISBN 12515:ISBN 12496:help 12476:2013 12463:ISBN 12391:PMID 12283:link 12054:ISBN 12003:ISBN 11978:ISBN 11953:ISBN 11928:ISBN 11903:ISBN 11833:ISBN 11726:2009 11677:ISBN 11583:ISBN 11556:2009 11414:ISBN 11372:ISBN 11347:ISBN 11320:ISBN 11295:ISBN 11264:ISBN 11239:ISBN 11036:and 10983:and 10891:, a 10828:> 10337:and 10329:and 10203:and 10165:left 9798:and 8987:and 8453:and 7609:= ±3 7601:= ±2 7593:= ±1 7577:= ±2 7569:= ±1 7553:= ±1 7463:and 7454:= ±1 7442:and 7426:and 7394:and 7338:and 7171:and 7072:has 7064:and 7056:and 7017:and 6990:and 6887:| ψ( 6833:| ψ( 6813:= 0) 5581:> 5534:and 5473:and 5331:real 5213:real 5141:real 5026:real 4966:and 4720:real 4522:real 4437:real 4168:real 3823:and 3649:real 3441:> 3258:< 3113:> 2970:< 2873:real 2829:real 2694:real 2612:= −1 2605:= +1 2570:The 2551:or − 2471:and 2359:... 2341:... 2336:... 2308:... 2281:... 2255:... 2230:... 2175:... 1969:The 1797:The 1773:The 1744:real 1630:and 1460:type 1352:Bohr 1250:and 1230:The 1071:The 1019:The 1000:and 963:) Φ( 951:) Φ( 947:) Θ( 939:) = 806:neon 763:spin 658:and 290:and 209:and 159:atom 49:, 2p 13194:By 13150:By 12626:doi 12455:doi 12426:doi 12381:doi 12369:373 12319:doi 12257:doi 12222:doi 12187:doi 12150:doi 12091:doi 12032:doi 12028:419 11872:doi 11806:doi 11794:121 11759:doi 11710:doi 11652:doi 11616:doi 11579:141 11540:doi 11498:doi 11456:doi 11044:= − 11034:= 0 11022:= 0 11015:= 2 10991:= + 10981:= 0 10969:= 0 10962:= 1 10921:1/2 10917:3/2 10901:1/2 10897:3/2 10831:137 10744:= 1 10679:). 10668:7p 10618:6p 10568:5p 10525:4p 10482:3p 10444:2p 10259:or 10171:). 8313:= 7 8203:= 6 8095:= 5 7973:= 4 7886:= 3 7824:= 2 7777:= 1 7715:xyz 7585:= 0 7561:= 0 7545:= 0 7537:= 0 7524:= 3 7519:f ( 7514:= 2 7509:d ( 7504:= 1 7499:p ( 7494:= 0 7489:s ( 7330:, p 7285:= 3 7248:= 2 7220:≥ 2 7209:= 1 7100:n-1 7088:= 1 7081:= 0 7045:= 0 7034:= 0 6921:). 6899:) | 6845:) | 3465:If 2356:... 2353:... 2350:... 2347:... 2344:... 2317:= 5 2290:= 4 2264:= 3 2239:= 2 2184:= 1 1904:= 2 1871:= 1 1746:or 1727:". 1638:). 1489:= 0 1482:= 1 1257:not 973:of 812:). 780:In 305:as 123:ɔːr 105:In 13360:: 12803:/ 12624:. 12614:43 12612:. 12488:: 12486:}} 12482:{{ 12461:. 12453:. 12424:. 12414:46 12412:. 12389:. 12379:. 12367:. 12363:. 12325:. 12317:. 12307:13 12305:. 12279:}} 12275:{{ 12263:. 12255:. 12245:85 12243:. 12220:. 12208:. 12185:. 12175:45 12173:. 12148:. 12138:93 12136:. 12132:. 12120:^ 12089:. 12079:41 12077:. 12026:. 11878:. 11870:. 11858:. 11804:. 11792:. 11788:. 11765:. 11757:. 11747:43 11745:. 11704:. 11700:. 11640:. 11612:44 11610:. 11606:. 11534:. 11530:. 11518:^ 11504:. 11496:. 11486:26 11484:. 11480:. 11468:^ 11454:. 11444:41 11442:. 11422:. 11393:, 11293:. 11209:. 11106:− 11090:− 11024:, 11017:, 10971:, 10964:, 10935:. 10732:. 10665:7p 10662:7p 10659:6d 10656:6d 10653:6d 10650:6d 10647:6d 10644:5f 10641:5f 10638:5f 10635:5f 10632:5f 10629:5f 10626:5f 10623:7s 10615:6p 10612:6p 10609:5d 10606:5d 10603:5d 10600:5d 10597:5d 10594:4f 10591:4f 10588:4f 10585:4f 10582:4f 10579:4f 10576:4f 10573:6s 10565:5p 10562:5p 10559:4d 10556:4d 10553:4d 10550:4d 10547:4d 10530:5s 10522:4p 10519:4p 10516:3d 10513:3d 10510:3d 10507:3d 10504:3d 10487:4s 10479:3p 10476:3p 10449:3s 10441:2p 10438:2p 10411:2s 10376:1s 10362:, 10358:, 10339:Mg 10335:Na 10331:Be 10327:Li 10264:-1 10138:59 10133:52 10128:46 10123:40 10118:35 10113:30 10108:10 10101:51 10096:45 10091:39 10086:34 10081:29 10076:25 10064:44 10059:38 10054:33 10049:28 10044:24 10039:20 10027:37 10022:32 10017:27 10012:23 10008:19 10005:16 9994:31 9989:26 9984:22 9980:18 9977:15 9974:12 9961:21 9957:17 9954:14 9951:11 9934:13 9931:10 9852:h 9849:g 9846:f 9843:d 9840:p 9837:s 9611:. 9412:23 9374:22 9336:21 9284:25 9221:20 9158:10 9104:13 9066:12 9028:11 8948:20 8885:10 8768:03 8730:02 8692:01 8664:. 8658:, 8654:, 8650:ψ( 8642:, 8638:ψ( 8570:: 8455:Cn 8451:Rg 8449:, 8447:Ds 8445:, 8443:Mt 8437:‡ 8431:Lr 8423:† 8417:* 8411:* 8405:* 8399:* 8393:* 8387:* 8381:* 8375:* 8369:* 8363:* 8357:* 8351:* 8345:* 8339:† 8333:† 8327:† 8304:* 8298:* 8292:* 8286:* 8280:* 8274:* 8268:* 8262:‡ 8256:‡ 8250:‡ 8244:‡ 8238:‡ 7759:(3 7746:−3 7707:yz 7699:xz 7671:xy 7663:yz 7655:xz 7617:s 7526:) 7516:) 7506:) 7496:) 7481:. 7467:−1 7460:+1 7446:−1 7439:+1 7378:. 7229:at 6967:, 6963:, 6959:ψ( 6951:, 6947:, 6943:ψ( 6933:, 6929:, 6925:ψ( 6911:, 6907:, 6903:ψ( 6895:, 6891:, 6872:, 6868:, 6864:ψ( 6849:| 6841:, 6837:, 4860:, 4757:21 4186:, 3799:. 3059:Re 2916:Im 2759:, 2593:. 2582:, 2578:, 2528:, 2508:= 2097:. 2028:, 1973:, 1966:. 1817:, 1794:. 1688:. 1673:. 1654:, 1474:. 1458:; 1366:, 1350:, 1166:. 1149:. 990:, 983:ℓm 959:Θ( 935:, 931:, 916:, 912:, 897:, 893:, 848:. 449:. 361:Cr 313:, 309:, 275:, 271:, 229:− 224:, 222:xy 211:−m 183:, 91:, 87:, 83:ψ( 75:, 71:, 67:ψ( 13071:e 13064:t 13057:v 12924:) 12922:s 12915:) 12913:m 12906:) 12904:ℓ 12897:) 12895:n 12839:e 12832:t 12825:v 12684:e 12677:t 12670:v 12632:. 12628:: 12620:: 12603:. 12584:. 12565:. 12542:. 12523:. 12498:) 12478:. 12457:: 12432:. 12428:: 12420:: 12397:. 12383:: 12375:: 12348:. 12333:. 12321:: 12313:: 12285:) 12271:. 12259:: 12251:: 12228:. 12224:: 12216:: 12210:8 12193:. 12189:: 12181:: 12158:. 12152:: 12144:: 12097:. 12093:: 12085:: 12062:. 12038:. 12034:: 12011:. 11986:. 11961:. 11936:. 11911:. 11886:. 11874:: 11866:: 11860:9 11841:. 11814:. 11808:: 11800:: 11773:. 11761:: 11753:: 11728:. 11712:: 11706:7 11685:. 11658:. 11654:: 11648:7 11622:. 11618:: 11591:. 11558:. 11542:: 11536:7 11512:. 11500:: 11492:: 11462:. 11458:: 11450:: 11380:. 11355:. 11328:. 11303:. 11272:. 11247:. 11111:1 11108:E 11104:2 11101:E 11095:1 11092:E 11088:2 11085:E 11079:2 11076:E 11070:1 11067:E 11055:2 11052:/ 11049:1 11041:s 11039:m 11031:ℓ 11027:m 11020:ℓ 11013:n 11002:2 10999:/ 10996:1 10988:s 10986:m 10978:ℓ 10974:m 10967:ℓ 10960:n 10873:Z 10869:Z 10865:Z 10861:Z 10825:Z 10809:c 10780:Z 10766:c 10760:Z 10757:= 10754:v 10742:n 10718:Z 10714:Z 10368:f 10364:d 10360:p 10356:s 10323:ℓ 10319:n 10315:ℓ 10296:i 10292:i 10270:2 10267:/ 10254:2 10251:/ 10248:1 10240:s 10238:m 10233:s 10231:m 10226:s 10224:m 10175:r 10071:9 10034:8 10001:7 9970:6 9948:9 9944:5 9928:8 9925:6 9921:4 9909:7 9906:5 9903:4 9899:3 9885:3 9882:2 9878:2 9862:1 9858:1 9832:n 9827:l 9786:n 9763:n 9719:3 9716:= 9693:2 9690:= 9627:n 9605:s 9597:j 9593:n 9579:n 9539:n 9519:n 9499:n 9479:1 9476:= 9473:n 9453:n 9408:u 9370:u 9332:u 9306:) 9292:0 9288:a 9281:= 9275:x 9272:a 9269:m 9264:r 9243:) 9229:0 9225:a 9218:= 9212:x 9209:a 9206:m 9201:r 9180:) 9166:0 9162:a 9155:= 9149:x 9146:a 9143:m 9138:r 9100:u 9062:u 9024:u 8997:s 8993:s 8989:d 8985:p 8977:s 8970:) 8956:0 8952:a 8945:= 8939:x 8936:a 8933:m 8928:r 8907:) 8893:0 8889:a 8882:= 8876:x 8873:a 8870:m 8865:r 8844:) 8830:0 8826:a 8822:2 8819:= 8813:x 8810:a 8807:m 8802:r 8764:u 8726:u 8688:u 8662:) 8660:φ 8656:θ 8652:r 8646:) 8644:θ 8640:r 8614:s 8607:s 8599:s 8551:, 8548:2 8542:, 8539:1 8533:= 8530:m 8508:z 8498:L 8474:0 8471:= 8468:m 8441:( 8311:n 8201:n 8093:n 7971:n 7884:n 7822:n 7775:n 7767:) 7765:y 7763:− 7761:x 7757:y 7754:f 7750:) 7748:y 7744:x 7742:( 7740:x 7737:f 7733:) 7731:y 7729:− 7727:x 7725:( 7723:z 7720:f 7712:f 7704:f 7696:f 7691:z 7688:f 7683:y 7681:− 7679:x 7676:d 7668:d 7660:d 7652:d 7647:z 7644:d 7639:y 7636:p 7631:x 7628:p 7623:z 7620:p 7607:m 7599:m 7591:m 7583:m 7575:m 7567:m 7559:m 7551:m 7543:m 7535:m 7522:ℓ 7512:ℓ 7502:ℓ 7492:ℓ 7474:0 7472:p 7465:p 7458:p 7452:m 7444:p 7437:p 7431:y 7428:p 7422:x 7419:p 7414:0 7412:p 7406:z 7403:p 7396:+ 7392:− 7372:ℓ 7368:n 7364:ℓ 7343:z 7340:p 7336:, 7333:y 7327:x 7324:p 7309:n 7305:n 7300:n 7283:n 7274:ℓ 7272:m 7246:n 7233:3 7224:n 7218:n 7207:n 7192:0 7189:= 7173:n 7169:ℓ 7164:ℓ 7162:m 7153:ℓ 7151:m 7147:ℓ 7131:Z 7127:n 7123:n 7116:m 7108:ℓ 7104:n 7086:ℓ 7079:ℓ 7074:ℓ 7070:ℓ 7066:ℓ 7062:n 7043:ℓ 7038:z 7032:m 7027:⟩ 7025:m 7021:m 7019:⟨ 7015:⟩ 7013:m 7009:m 7007:⟨ 7003:m 6999:m 6994:m 6992:− 6988:m 6971:) 6969:φ 6965:θ 6961:r 6955:) 6953:φ 6949:θ 6945:r 6937:) 6935:φ 6931:θ 6927:r 6915:) 6913:φ 6909:θ 6905:r 6897:φ 6893:θ 6889:r 6883:ψ 6876:) 6874:φ 6870:θ 6866:r 6853:| 6851:ψ 6843:φ 6839:θ 6835:r 6818:n 6811:m 6807:ℓ 6803:n 6801:( 6771:) 6766:2 6762:y 6758:3 6750:2 6746:x 6742:( 6739:x 6734:f 6709:) 6704:2 6700:y 6691:2 6687:x 6683:( 6680:z 6675:f 6648:2 6644:z 6640:x 6635:f 6608:3 6604:z 6598:f 6571:2 6567:z 6563:y 6558:f 6533:z 6530:y 6527:x 6522:f 6497:) 6492:2 6488:y 6479:2 6475:x 6471:3 6468:( 6465:y 6460:f 6437:3 6434:= 6402:2 6398:y 6389:2 6385:x 6379:d 6354:z 6351:x 6346:d 6319:2 6315:z 6309:d 6284:z 6281:y 6276:d 6251:y 6248:x 6243:d 6218:2 6215:= 6183:x 6178:p 6153:z 6148:p 6123:y 6118:p 6091:1 6088:= 6055:s 6027:0 6024:= 5996:3 5993:+ 5990:= 5987:m 5974:3 5968:= 5965:m 5937:2 5934:+ 5931:= 5928:m 5915:2 5909:= 5906:m 5878:1 5875:+ 5872:= 5869:m 5856:1 5850:= 5847:m 5819:0 5816:= 5813:m 5785:1 5782:+ 5779:= 5776:m 5768:+ 5763:1 5757:= 5754:m 5726:2 5723:+ 5720:= 5717:m 5709:+ 5704:2 5698:= 5695:m 5667:3 5664:+ 5661:= 5658:m 5650:+ 5645:3 5639:= 5636:m 5604:g 5584:3 5552:1 5544:p 5520:1 5517:+ 5512:p 5488:y 5483:p 5459:x 5454:p 5420:) 5414:1 5411:+ 5407:f 5403:n 5395:1 5388:f 5384:n 5380:( 5373:2 5369:1 5364:= 5357:2 5353:z 5349:x 5345:f 5341:n 5336:= 5326:1 5323:+ 5320:, 5317:3 5314:, 5311:n 5298:) 5292:1 5289:+ 5284:p 5279:n 5271:1 5263:p 5258:n 5254:( 5247:2 5243:1 5238:= 5233:x 5228:p 5223:n 5218:= 5208:1 5205:+ 5202:, 5199:1 5196:, 5193:n 5179:0 5174:p 5169:2 5166:= 5161:z 5156:p 5151:n 5146:= 5136:0 5133:, 5130:1 5127:, 5124:n 5111:) 5105:1 5102:+ 5097:p 5092:n 5089:+ 5084:1 5076:p 5071:n 5067:( 5060:2 5056:i 5051:= 5046:y 5041:p 5036:n 5031:= 5021:1 5015:, 5012:1 5009:, 5006:n 4954:n 4934:z 4914:r 4911:, 4908:z 4888:z 4868:y 4848:x 4821:3 4817:r 4812:) 4807:2 4803:r 4794:2 4790:z 4786:5 4783:( 4777:x 4761:2 4749:4 4746:1 4739:3 4736:, 4733:n 4729:R 4725:= 4715:1 4712:+ 4709:, 4706:3 4703:, 4700:n 4672:r 4668:/ 4664:z 4653:4 4649:/ 4645:3 4638:1 4635:, 4632:n 4628:R 4624:= 4619:0 4616:, 4613:1 4610:, 4607:n 4573:r 4570:y 4555:4 4551:3 4543:1 4540:, 4537:n 4533:R 4527:= 4517:1 4511:, 4508:1 4505:, 4502:n 4488:r 4485:x 4470:4 4466:3 4458:1 4455:, 4452:n 4448:R 4442:= 4432:1 4429:+ 4426:, 4423:1 4420:, 4417:n 4381:2 4377:z 4373:+ 4368:2 4364:y 4360:+ 4355:2 4351:x 4345:= 4342:r 4322:r 4318:/ 4314:) 4311:y 4308:i 4302:x 4299:( 4288:8 4284:/ 4280:3 4273:1 4270:, 4267:n 4263:R 4256:= 4251:1 4243:1 4239:Y 4233:1 4230:, 4227:n 4223:R 4219:= 4214:1 4208:, 4205:1 4202:, 4199:n 4163:1 4157:, 4154:1 4151:, 4148:n 4120:m 4080:n 4058:1 4052:, 4049:1 4046:, 4043:2 4035:= 4030:1 4022:p 4017:2 3969:6 3966:, 3963:5 3960:, 3957:4 3954:, 3951:3 3948:, 3945:2 3942:, 3939:1 3936:, 3933:0 3891:m 3888:, 3882:, 3879:n 3851:m 3811:n 3785:m 3776:Y 3753:m 3746:Y 3725:) 3719:, 3713:( 3708:m 3701:Y 3697:) 3694:r 3691:( 3686:l 3683:n 3679:R 3675:= 3672:) 3666:, 3660:, 3657:r 3654:( 3644:m 3641:, 3635:, 3632:n 3607:) 3604:r 3601:( 3596:l 3593:n 3589:R 3568:) 3562:, 3556:( 3551:m 3542:Y 3538:) 3535:r 3532:( 3527:l 3524:n 3520:R 3516:= 3513:) 3507:, 3501:, 3498:r 3495:( 3490:m 3487:, 3481:, 3478:n 3444:0 3438:m 3427:) 3420:| 3416:m 3412:| 3408:, 3402:, 3399:n 3389:m 3385:) 3381:1 3375:( 3372:+ 3366:| 3362:m 3358:| 3351:, 3345:, 3342:n 3333:( 3326:2 3322:1 3313:0 3310:= 3307:m 3294:| 3290:m 3286:| 3282:, 3276:, 3273:n 3261:0 3255:m 3244:) 3237:| 3233:m 3229:| 3225:, 3219:, 3216:n 3206:m 3202:) 3198:1 3192:( 3183:| 3179:m 3175:| 3168:, 3162:, 3159:n 3150:( 3143:2 3139:i 3131:{ 3126:= 3116:0 3110:m 3099:} 3093:| 3089:m 3085:| 3081:, 3075:, 3072:n 3064:{ 3053:m 3049:) 3045:1 3039:( 3034:2 3025:0 3022:= 3019:m 3006:| 3002:m 2998:| 2994:, 2988:, 2985:n 2973:0 2967:m 2956:} 2950:| 2946:m 2942:| 2938:, 2932:, 2929:n 2921:{ 2910:m 2906:) 2902:1 2896:( 2891:2 2883:{ 2878:= 2868:m 2865:, 2859:, 2856:n 2824:m 2821:, 2815:, 2812:n 2787:m 2767:l 2747:n 2725:m 2722:, 2716:, 2713:n 2674:x 2669:p 2645:1 2640:p 2610:m 2603:m 2598:z 2590:s 2588:m 2584:m 2580:ℓ 2576:n 2562:2 2559:/ 2556:1 2546:2 2543:/ 2540:1 2532:s 2530:m 2519:2 2516:/ 2513:1 2506:s 2485:0 2482:= 2459:2 2456:= 2453:n 2413:n 2373:n 2321:0 2315:n 2294:0 2288:n 2268:0 2262:n 2243:0 2237:n 2208:0 2205:= 2196:m 2182:n 2169:ℓ 2161:ℓ 2153:ℓ 2145:ℓ 2137:ℓ 2109:m 2073:m 2037:m 1982:m 1960:ℓ 1946:1 1943:= 1920:0 1917:= 1902:n 1887:0 1884:= 1869:n 1854:1 1846:0 1842:n 1829:0 1819:ℓ 1814:0 1811:n 1806:n 1802:ℓ 1786:n 1778:n 1721:ℓ 1717:n 1709:n 1705:n 1701:n 1693:n 1665:ℓ 1663:m 1657:ℓ 1651:n 1587:n 1564:ℓ 1557:. 1540:y 1535:e 1532:p 1529:y 1526:t 1520:X 1503:ℓ 1494:ℓ 1487:ℓ 1480:n 1472:ℓ 1456:n 1449:X 1428:e 1425:p 1422:y 1419:t 1414:X 1384:n 1332:n 1328:n 1324:n 1320:n 1316:n 1292:n 1217:ħ 1122:. 1106:2 1102:r 1091:e 1068:. 1054:r 1044:e 1029:r 1013:) 1011:r 1009:( 1007:R 1002:m 998:ℓ 994:) 992:φ 988:θ 986:( 979:Y 967:) 965:φ 961:θ 955:) 953:φ 949:θ 945:r 943:( 941:R 937:φ 933:θ 929:r 927:( 925:ψ 920:) 918:z 914:y 910:x 908:( 901:) 899:φ 895:θ 891:r 889:( 866:g 810:0 691:l 687:m 666:l 646:n 629:2 626:/ 623:1 604:l 600:m 579:l 559:n 535:i 523:5 520:/ 517:3 507:5 504:/ 501:2 491:2 488:/ 485:1 475:2 472:/ 469:1 440:. 353:n 324:ℓ 292:3 286:ℓ 253:s 249:m 231:y 227:x 213:ℓ 206:ℓ 204:m 191:ℓ 189:m 185:ℓ 181:n 141:/ 138:l 135:ə 132:t 129:ɪ 126:b 120:ˈ 117:/ 113:( 95:) 93:z 89:y 85:x 79:) 77:z 73:y 69:x 58:z 52:y 46:x 34:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index