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 However, this period was immediately superseded by the full three-dimensional wave mechanics of 1926.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.
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:
17:
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:
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5634:
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5625:
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5601:
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5535:
5515:
5510:
5509:
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5486:
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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:
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5079:
5074:
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5053:
5044:
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5033:
5024:
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4971:
4968:
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4951:
4948:
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4905:
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4885:
4882:
4881:
4865:
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4845:
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4801:
4792:
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4743:
4731:
4727:
4718:
4698:
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4689:
4688:
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4647:
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4630:
4626:
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4500:
4493:
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4401:
4379:
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4366:
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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:
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3910:
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3877:
3873:
3871:
3868:
3867:
3848:
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3828:
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3824:
3808:
3805:
3804:
3783:
3778:
3772:
3769:
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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:
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
18:P-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::
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12461:.
12453:.
12424:.
12414:46
12412:.
12389:.
12379:.
12367:.
12363:.
12325:.
12317:.
12307:13
12305:.
12279:}}
12275:{{
12263:.
12255:.
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12243:.
12220:.
12208:.
12185:.
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12173:.
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12138:93
12136:.
12132:.
12120:^
12089:.
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12077:.
12026:.
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11870:.
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11792:.
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11765:.
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11745:.
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11700:.
11640:.
11612:44
11610:.
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11534:.
11530:.
11518:^
11504:.
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11484:.
11480:.
11468:^
11454:.
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11442:.
11422:.
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11293:.
11209:.
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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
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9066:12
9028:11
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8885:10
8768:03
8730:02
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8664:.
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8654:,
8650:ψ(
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8570::
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8423:†
8417:*
8411:*
8405:*
8399:*
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8387:*
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8280:*
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7746:−3
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3059:Re
2916:Im
2759:,
2593:.
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2528:,
2508:=
2097:.
2028:,
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1966:.
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1688:.
1673:.
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1458:;
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990:,
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959:Θ(
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361:Cr
313:,
309:,
275:,
271:,
229:−
224:,
222:xy
211:−m
183:,
91:,
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83:ψ(
75:,
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67:ψ(
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13064:t
13057:v
12924:)
12922:s
12915:)
12913:m
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12904:ℓ
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12895:n
12839:e
12832:t
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12632:.
12628::
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11052:/
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11031:ℓ
11027:m
11020:ℓ
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10999:/
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10978:ℓ
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10960:n
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10869:Z
10865:Z
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10757:=
10754:v
10742:n
10718:Z
10714:Z
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10364:d
10360:p
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10323:ℓ
10319:n
10315:ℓ
10296:i
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10267:/
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10240:s
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10226:s
10224:m
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10071:9
10034:8
10001:7
9970:6
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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
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9229:0
9225:a
9218:=
9212:x
9209:a
9206:m
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9166:0
9162:a
9155:=
9149:x
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9062:u
9024:u
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8977:s
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8956:0
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8945:=
8939:x
8936:a
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8907:)
8893:0
8889:a
8882:=
8876:x
8873:a
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8844:)
8830:0
8826:a
8822:2
8819:=
8813:x
8810:a
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8726:u
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8662:)
8660:φ
8656:θ
8652:r
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8614:s
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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
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7767:)
7765:y
7763:−
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7583:m
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7502:ℓ
7492:ℓ
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7465:p
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7396:+
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7364:ℓ
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7340:p
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7300:n
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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
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7038:z
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7025:m
7021:m
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6969:φ
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6218:2
6215:=
6183:x
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6091:1
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6055:s
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5996:3
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5987:m
5974:3
5968:=
5965:m
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5934:+
5931:=
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5847:m
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5720:=
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5667:3
5664:+
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5645:3
5639:=
5636:m
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5584:3
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5520:1
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5420:)
5414:1
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5380:(
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5326:1
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5320:,
5317:3
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5218:=
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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
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910:x
908:(
901:)
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891:r
889:(
866:g
810:0
691:l
687:m
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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:)
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