863:
This discrete energy spectrum resulted from the solution of the quantum mechanical problem on the electron motion in the
Coulomb field, coincides with the spectrum that was obtained with the help application of the BohrâSommerfeld quantization rules to the classical equations. The radial quantum
259:
reduces to the three equations that when solved lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The principal quantum number arose in the solution of the radial part of the wave equation as shown below.
827:
398:
663:
475:
288:
512:
represents the relative overall energy of each orbital. The energy level of each orbital increases as its distance from the nucleus increases. The sets of orbitals with the same
630:
205:, distinguishing between different energy levels. With the development of modern quantum mechanics, the simple Bohr model was replaced with a more complex theory of
854:
1075:
150:
In a simplistic one-electron model described below, the total energy of an electron is a negative inverse quadratic function of the principal quantum number
1182:
424:
1068:
1177:
1048:
1012:
1203:
1061:
410:. Schrödinger's equation developed the idea from a flat two-dimensional Bohr atom to the three-dimensional wavefunction model.
995:
112:
17:
1110:
1029:
933:
590:
822:{\displaystyle E_{n}=-{\frac {Z^{2}\hbar ^{2}}{2m_{0}a_{0}^{2}n^{2}}}=-{\frac {Z^{2}e^{4}m_{0}}{2\hbar ^{2}n^{2}}},}
107:
increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus. For higher
251:. Two electrons belonging to the same atom cannot have the same values for all four quantum numbers, due to the
406:
can take only positive integer values. The concept of energy levels and notation were taken from the earlier
264:
223:
There is a set of quantum numbers associated with the energy states of the atom. The four quantum numbers
1295:
1198:
393:{\displaystyle E_{n}={\frac {E_{1}}{n^{2}}}={\frac {-13.6{\text{ eV}}}{n^{2}}},\quad n=1,2,3,\ldots }
252:
1305:
1139:
494:
155:
72:
1300:
1148:
897:
79:
983:
256:
162: > 1. In more complex systemsâthose having forces other than the nucleusâelectron
1084:
1021:
413:
In the Bohr model, the allowed orbits were derived from quantized (discrete) values of orbital
167:
653:
832:
523:
The minimum energy exchanged during any waveâmatter interaction is the product of the wave
8:
1157:
913:
89:
218:
1049:
Periodic Table Applet: showing principal and azimuthal quantum number for each element
1260:
1229:
1105:
1025:
991:
657:
540:
61:
31:
1274:
1245:
1208:
498:
497:, but the energy levels are accurate and classically they correspond to the sum of
490:
414:
917:
546:
In the notation of the periodic table, the main shells of electrons are labeled:
528:
486:
170:. For multielectron atoms this splitting results in "subshells" parametrized by
1122:
1100:
1095:
969:
901:
889:
646:
517:
502:
248:
206:
140:
57:
45:
481:= 1, 2, 3, ... and is called the principal quantum number, and
1289:
1250:
1224:
909:
244:
240:
183:
163:
175:
135:
electron states are more numerous. Accounting for two states of spin, each
209:. However, the modern theory still requires the principal quantum number.
1053:
857:
531:. This causes the wave to display particle-like packets of energy called
282:
68:
1269:
407:
202:
67:
Apart from the principal quantum number, the other quantum numbers for
578:
The principal quantum number is related to the radial quantum number,
881:
524:
191:
49:
988:
Atomic spectroscopy. Introduction of theory to
Hyperfine Structure
864:
number determines the number of nodes of the radial wave function
532:
201:
The principal quantum number was first created for use in the
187:
652:
The definite total energy for a particle motion in a common
285:
energies of the electron in the hydrogen atom are given by:
535:. The difference between energy levels that have different
53:
489:. This formula is not correct in quantum mechanics as the
888: = 1, 2, 3, 4, 5, 6, 7 are used in relation to the
924:
on order of hundreds; values up to 766 were detected.
470:{\displaystyle L=n\cdot \hbar =n\cdot {h \over 2\pi }}
896: = 8 (and possibly 9) for yet-undiscovered
835:
666:
593:
427:
291:
1183:
Electron configurations of the elements (data page)
848:
821:
624:
469:
392:
56:to describe that electron's state. Its values are
1287:
975:
263:The Schrödinger wave equation describes energy
968:) is degenerate, assuming absence of external
1069:
243:of a single electron in an atom, called its
27:Number assigned to each electron in an atom
1083:
1076:
1062:
274:and a definite total energy, the value of
111:the electron is farther from the nucleus,
131: â 1 inclusively, hence higher-
1178:Periodic table (electron configurations)
1010:
1004:
575:based on the principal quantum number.
182:alone gradually becomes inadequate for
98:
14:
1288:
981:
1057:
127:(azimuthal) values ranging from 0 to
952:Here we ignore spin. Accounting for
636:is the azimuthal quantum number and
203:semiclassical Bohr model of the atom
946:
908:sometimes occur for description of
892:theory, with expected inclusion of
24:
516:value are often referred to as an
25:
1317:
1111:Introduction to quantum mechanics
1042:
934:Introduction to quantum mechanics
440:
198: = 19) and afterwards.
267:with corresponding real numbers
239:specify the complete and unique
625:{\displaystyle n=n_{r}+\ell +1}
362:
493:magnitude is described by the
13:
1:
939:
508:The principal quantum number
212:
649:in the radial wavefunction.
7:
1171:Ground-state configurations
1011:Tennyson, Jonathan (2005).
927:
10:
1322:
1140:Azimuthal quantum number (
1131:Principal quantum number (
982:Andrew, A. V. (2006). "2.
645:is equal to the number of
421:according to the equation
216:
190:) and fails completely on
1259:
1238:
1217:
1199:Pauli exclusion principle
1191:
1170:
1149:Magnetic quantum number (
1121:
1091:
1014:Astronomical Spectroscopy
920:spectral lines involving
875:
257:Schrödinger wave equation
253:Pauli exclusion principle
495:azimuthal quantum number
156:degenerate energy levels
73:azimuthal quantum number
36:principal quantum number
960:orbital (determined by
143:can accommodate up to 2
80:magnetic quantum number
60:(from one) making it a
1085:Electron configuration
1022:Imperial College Press
912:. Observations of the
850:
823:
626:
471:
408:Bohr model of the atom
394:
1239:Bonding participation
1158:Spin quantum number (
851:
849:{\displaystyle a_{0}}
824:
627:
472:
395:
18:Radial quantum number
984:Schrödinger equation
833:
664:
591:
425:
289:
115:. For each value of
99:Overview and history
914:interstellar medium
735:
90:spin quantum number
846:
819:
721:
622:
527:multiplied by the
467:
390:
219:Hydrogen-like atom
71:electrons are the
1296:Quantum chemistry
1283:
1282:
1261:Electron counting
1230:Unpaired electron
1106:Quantum mechanics
997:978-0-387-25573-6
898:period 8 elements
814:
747:
658:discrete spectrum
541:emission spectrum
505:of the electron.
465:
357:
344:
327:
186:starting from 5 (
174:. Description of
62:discrete variable
48:assigned to each
44:) is one of four
32:quantum mechanics
16:(Redirected from
1313:
1275:18-electron rule
1246:Valence electron
1218:Electron pairing
1209:Aufbau principle
1192:Electron filling
1161:
1152:
1143:
1134:
1078:
1071:
1064:
1055:
1054:
1036:
1035:
1019:
1008:
1002:
1001:
979:
973:
950:
855:
853:
852:
847:
845:
844:
828:
826:
825:
820:
815:
813:
812:
811:
802:
801:
788:
787:
786:
777:
776:
767:
766:
756:
748:
746:
745:
744:
734:
729:
720:
719:
706:
705:
704:
695:
694:
684:
676:
675:
631:
629:
628:
623:
609:
608:
543:of the element.
491:angular momentum
476:
474:
473:
468:
466:
464:
453:
415:angular momentum
399:
397:
396:
391:
358:
356:
355:
346:
345:
342:
333:
328:
326:
325:
316:
315:
306:
301:
300:
21:
1321:
1320:
1316:
1315:
1314:
1312:
1311:
1310:
1306:Quantum numbers
1286:
1285:
1284:
1279:
1255:
1234:
1213:
1187:
1166:
1159:
1150:
1141:
1132:
1123:Quantum numbers
1117:
1087:
1082:
1045:
1040:
1039:
1032:
1017:
1009:
1005:
998:
990:. p. 274.
980:
976:
951:
947:
942:
930:
918:atomic hydrogen
878:
840:
836:
834:
831:
830:
807:
803:
797:
793:
789:
782:
778:
772:
768:
762:
758:
757:
755:
740:
736:
730:
725:
715:
711:
707:
700:
696:
690:
686:
685:
683:
671:
667:
665:
662:
661:
660:, is given by:
644:
604:
600:
592:
589:
588:
586:
573:
529:Planck constant
487:Planck constant
457:
452:
426:
423:
422:
351:
347:
341:
334:
332:
321:
317:
311:
307:
305:
296:
292:
290:
287:
286:
279:
272:
221:
215:
207:atomic orbitals
101:
86:
58:natural numbers
46:quantum numbers
28:
23:
22:
15:
12:
11:
5:
1319:
1309:
1308:
1303:
1301:Atomic physics
1298:
1281:
1280:
1278:
1277:
1272:
1266:
1264:
1257:
1256:
1254:
1253:
1248:
1242:
1240:
1236:
1235:
1233:
1232:
1227:
1221:
1219:
1215:
1214:
1212:
1211:
1206:
1201:
1195:
1193:
1189:
1188:
1186:
1185:
1180:
1174:
1172:
1168:
1167:
1165:
1164:
1155:
1146:
1137:
1127:
1125:
1119:
1118:
1116:
1115:
1114:
1113:
1103:
1101:Atomic orbital
1098:
1096:Electron shell
1092:
1089:
1088:
1081:
1080:
1073:
1066:
1058:
1052:
1051:
1044:
1043:External links
1041:
1038:
1037:
1030:
1024:. p. 39.
1003:
996:
974:
970:magnetic field
944:
943:
941:
938:
937:
936:
929:
926:
910:excited states
902:atomic physics
890:electron shell
877:
874:
843:
839:
818:
810:
806:
800:
796:
792:
785:
781:
775:
771:
765:
761:
754:
751:
743:
739:
733:
728:
724:
718:
714:
710:
703:
699:
693:
689:
682:
679:
674:
670:
640:
621:
618:
615:
612:
607:
603:
599:
596:
582:
548:
539:determine the
518:electron shell
503:kinetic energy
463:
460:
456:
451:
448:
445:
442:
439:
436:
433:
430:
402:The parameter
389:
386:
383:
380:
377:
374:
371:
368:
365:
361:
354:
350:
340:
337:
331:
324:
320:
314:
310:
304:
299:
295:
277:
270:
217:Main article:
214:
211:
184:atomic numbers
166:âthese levels
100:
97:
84:
26:
9:
6:
4:
3:
2:
1318:
1307:
1304:
1302:
1299:
1297:
1294:
1293:
1291:
1276:
1273:
1271:
1268:
1267:
1265:
1262:
1258:
1252:
1251:Core electron
1249:
1247:
1244:
1243:
1241:
1237:
1231:
1228:
1226:
1225:Electron pair
1223:
1222:
1220:
1216:
1210:
1207:
1205:
1202:
1200:
1197:
1196:
1194:
1190:
1184:
1181:
1179:
1176:
1175:
1173:
1169:
1163:
1156:
1154:
1147:
1145:
1138:
1136:
1129:
1128:
1126:
1124:
1120:
1112:
1109:
1108:
1107:
1104:
1102:
1099:
1097:
1094:
1093:
1090:
1086:
1079:
1074:
1072:
1067:
1065:
1060:
1059:
1056:
1050:
1047:
1046:
1033:
1031:1-86094-513-9
1027:
1023:
1016:
1015:
1007:
999:
993:
989:
985:
978:
971:
967:
963:
959:
955:
949:
945:
935:
932:
931:
925:
923:
919:
915:
911:
907:
903:
899:
895:
891:
887:
883:
873:
871:
867:
861:
859:
841:
837:
816:
808:
804:
798:
794:
790:
783:
779:
773:
769:
763:
759:
752:
749:
741:
737:
731:
726:
722:
716:
712:
708:
701:
697:
691:
687:
680:
677:
672:
668:
659:
655:
654:Coulomb field
650:
648:
643:
639:
635:
619:
616:
613:
610:
605:
601:
597:
594:
585:
581:
576:
571:
567:
563:
559:
555:
551:
547:
544:
542:
538:
534:
530:
526:
521:
519:
515:
511:
506:
504:
500:
496:
492:
488:
484:
480:
461:
458:
454:
449:
446:
443:
437:
434:
431:
428:
420:
416:
411:
409:
405:
400:
387:
384:
381:
378:
375:
372:
369:
366:
363:
359:
352:
348:
338:
335:
329:
322:
318:
312:
308:
302:
297:
293:
284:
280:
273:
266:
261:
258:
254:
250:
246:
245:wave function
242:
241:quantum state
238:
234:
230:
226:
220:
210:
208:
204:
199:
197:
193:
189:
185:
181:
177:
176:energy levels
173:
169:
165:
164:Coulomb force
161:
157:
154:, leading to
153:
148:
146:
142:
138:
134:
130:
126:
122:
118:
114:
110:
106:
96:
94:
91:
87:
81:
77:
74:
70:
65:
63:
59:
55:
51:
47:
43:
42:
37:
33:
19:
1130:
1013:
1006:
987:
977:
965:
961:
957:
953:
948:
921:
905:
893:
885:
879:
869:
865:
862:
651:
641:
637:
633:
583:
579:
577:
574:
569:
565:
561:
557:
553:
549:
545:
536:
522:
513:
509:
507:
482:
478:
418:
412:
403:
401:
275:
268:
262:
236:
232:
228:
224:
222:
200:
195:
179:
171:
159:
151:
149:
144:
136:
132:
128:
124:
120:
116:
108:
104:
102:
92:
82:
75:
66:
40:
39:
38:(symbolized
35:
29:
1204:Hund's rule
858:Bohr radius
656:and with a
283:bound state
265:eigenstates
147:electrons.
1290:Categories
1270:Octet rule
1020:. London:
940:References
572:= 3), etc.
213:Derivation
119:there are
113:on average
88:, and the
904:, higher
884:, values
882:chemistry
795:ℏ
753:−
698:ℏ
681:−
614:ℓ
525:frequency
499:potential
462:π
450:⋅
441:ℏ
438:⋅
388:…
336:−
192:potassium
178:based on
158:for each
123:accepted
928:See also
343: eV
50:electron
916:reveal
856:is the
485:is the
255:. The
249:orbital
1028:
994:
876:Values
829:where
632:where
587:, by:
564:= 2),
556:= 1),
533:quanta
477:where
281:. The
235:, and
78:, the
52:in an
34:, the
1263:rules
1018:(PDF)
958:every
900:. In
647:nodes
188:boron
168:split
141:shell
69:bound
1026:ISBN
992:ISBN
964:and
501:and
339:13.6
54:atom
986:".
880:In
872:).
247:or
103:As
30:In
1292::
956:,
860:.
520:.
417:,
231:,
227:,
95:.
64:.
1162:)
1160:s
1153:)
1151:m
1144:)
1142:â
1135:)
1133:n
1077:e
1070:t
1063:v
1034:.
1000:.
972:.
966:â
962:n
954:s
922:n
906:n
894:n
886:n
870:r
868:(
866:R
842:0
838:a
817:,
809:2
805:n
799:2
791:2
784:0
780:m
774:4
770:e
764:2
760:Z
750:=
742:2
738:n
732:2
727:0
723:a
717:0
713:m
709:2
702:2
692:2
688:Z
678:=
673:n
669:E
642:r
638:n
634:â
620:1
617:+
611:+
606:r
602:n
598:=
595:n
584:r
580:n
570:n
568:(
566:M
562:n
560:(
558:L
554:n
552:(
550:K
537:n
514:n
510:n
483:h
479:n
459:2
455:h
447:n
444:=
435:n
432:=
429:L
419:L
404:n
385:,
382:3
379:,
376:2
373:,
370:1
367:=
364:n
360:,
353:2
349:n
330:=
323:2
319:n
313:1
309:E
303:=
298:n
294:E
278:n
276:E
271:n
269:E
237:s
233:m
229:â
225:n
196:Z
194:(
180:n
172:â
160:n
152:n
145:n
139:-
137:n
133:n
129:n
125:â
121:n
117:n
109:n
105:n
93:s
85:l
83:m
76:â
41:n
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.