20:
1334:
92:
770:
1531:
1096:
1540:
A simplified explanation for the effective charge of a nucleus being one less than its actual charge is that an unpaired electron in the K-shell screens it. An elaborate discussion criticizing
Moseley's interpretation of screening can be found in a paper by Whitaker which is repeated in most modern
46:
in 1913–1914. Until
Moseley's work, "atomic number" was merely an element's place in the periodic table and was not known to be associated with any measurable physical quantity. In brief, the law states that the square root of the frequency of the emitted X-ray is approximately proportional to the
581:
1544:
A list of experimentally found and theoretically calculated X-ray transition energies is available at NIST. Nowadays, theoretical energies are computed with much greater accuracy than
Moseley's law allows, using modern computational models such as the Dirac–Fock method (the
1343:
1329:{\displaystyle E=h\nu =E_{\text{i}}-E_{\text{f}}={\frac {m_{\text{e}}q_{\text{e}}^{4}}{8h^{2}\varepsilon _{0}^{2}}}\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right)(Z-1)^{2}\approx {\frac {3}{4}}(Z-1)^{2}\times 13.6\ \mathrm {eV} .}
507:
385:
765:{\displaystyle E=h\nu =E_{\text{i}}-E_{\text{f}}={\frac {m_{\text{e}}q_{\text{e}}^{2}q_{Z}^{2}}{8h^{2}\varepsilon _{0}^{2}}}\left({\frac {1}{n_{\text{f}}^{2}}}-{\frac {1}{n_{\text{i}}^{2}}}\right),}
245:
23:
Photographic recording of Kα and Kβ X-ray emission lines for a range of elements; note that for the dispersive element used, the line position is proportional to the wavelength (not energy)
1035:
82:
1526:{\displaystyle \nu ={\frac {E}{h}}={\frac {m_{\text{e}}q_{\text{e}}^{4}}{8h^{3}\varepsilon _{0}^{2}}}{\frac {3}{4}}(Z-1)^{2}\approx (Z-1)^{2}\times (2.47\cdot 10^{15}\ \mathrm {Hz} ).}
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Since the spectral emissions for the lighter elements would be in the soft X-ray range (absorbed by air), the spectrometry apparatus had to be enclosed inside a
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143:. Details of the experimental setup are documented in the journal articles "The High-Frequency Spectra of the Elements" Part I and Part II.
113:, but in a few famous cases the physical properties of two elements suggested that the heavier ought to precede the lighter. An example is
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574:
the square root of the X-ray frequency plotted against the atomic number. This formula can be explained based on the
1753:
A. M. Lesk (1980). "Reinterpretation of
Moseley's experiments relating K alpha line frequencies and atomic number".
2319:
2159:
2047:
1000:
131:
to study the elements, and the results of their experiments led to organizing the periodic table by proton count.
1986:
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2137:
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Whitaker, M. A. B. (1999). "The Bohr–Moseley synthesis and a simple model for atomic X-ray energies".
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2017:
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2012:
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Following Bohr's lead, Moseley found that for the spectral lines, this relationship could be
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1861:(Reproduction of the original Moseley diagram showing the square root frequency dependence)
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1996:
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1611:. Smithsonian Libraries. London-Edinburgh: London : Taylor & Francis: 1024–1034.
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253:
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Mosley's law was an important step in the development of the understanding of the atom.
1572:, a similar phenomenon with increased X-ray yield from species of higher atomic number.
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295:
275:
128:
1718:
K. R. Naqvi (1996). "The physical (in)significance of
Moseley's screening parameter".
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are constants that depend on the type of line (that is, K, L, etc. in X-ray notation)
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31:
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The London, Edinburgh and Dublin
Philosophical Magazine and Journal of Science
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constant that reduced (or "screened") the nucleus charge, Bohr's formula for
575:
91:
502:{\displaystyle A=\left({\frac {1}{2^{2}}}-{\frac {1}{3^{2}}}\right)\cdot }
380:{\displaystyle A=\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right)\cdot }
1976:
2100:
42:. The law had been discovered and published by the English physicist
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1680:. Vol. 1, Part 1. New York: Springer-Verlag. pp. 193–196.
1647:"The High-Frequency Spectra of the Elements. Part II"
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is an effective charge of the nucleus, expressed as
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is the frequency of the observed X-ray emission line
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240:{\displaystyle \nu =A\cdot \left(Z-b\right)^{2}}
1340:to convert to the frequency units, one obtains
997:is the quantum number of initial energy level (
1881:
8:
1848:Oxford Physics Teaching - History Archive, "
1678:The historical development of quantum theory
1601:"The High-Frequency Spectra of the Elements"
1030:{\displaystyle n_{\text{i}}>n_{\text{f}}}
178:) were indeed related to the atomic number,
968:is the quantum number of final energy level
570:Moseley derived his formula empirically by
77:{\displaystyle {\sqrt {\nu }}\varpropto Z.}
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1066:Taking into account the empirically found
1832:"NIST X-ray Transition Energies Database"
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1707:. G. Bell and Sons, Ltd. pp. 75–87.
1588:
1566:, concerning the modern periodic table.
16:Law concerning X-rays emitted by atoms
117:having the atomic weight of 58.9 and
7:
1513:
1510:
1319:
1316:
188:by a simple formula, later called
121:having the atomic weight of 58.7.
106:was roughly ordered by increasing
14:
795:{\displaystyle \varepsilon _{0}}
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1:
1645:Moseley, Henry G. J. (1914).
1599:Moseley, Henry G. J. (1913).
1850:Exhibit 12 - Moseley's graph
1704:X Rays and Crystal Structure
990:{\displaystyle n_{\text{i}}}
961:{\displaystyle n_{\text{f}}}
859:{\displaystyle q_{\text{e}}}
827:{\displaystyle m_{\text{e}}}
1790:European Journal of Physics
1755:American Journal of Physics
1720:American Journal of Physics
1570:Auger electron spectroscopy
2383:
2160:X-Ray Fluorescence Imaging
2048:Anomalous X-ray scattering
1810:10.1088/0143-0807/20/3/312
933:{\displaystyle (Z-b)q_{e}}
804:permittivity of free space
127:and other physicists used
2352:Eponymous laws of physics
1617:10.1080/14786441308635052
1987:Synchrotron light source
1576:Discovery of the neutron
1086:{\displaystyle K\alpha }
554:{\displaystyle L\alpha }
429:{\displaystyle K\alpha }
167:{\displaystyle K\alpha }
2006:Interaction with matter
1965:Sources and instruments
1336:Dividing both sides by
151:Moseley found that the
104:historic periodic table
98:, holding an X-ray tube
2138:Diffraction tomography
1651:Philosophical Magazine
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2249:X-ray crystallography
2118:Soft x-ray microscopy
2086:Panoramic radiography
1926:Synchrotron radiation
1701:Bragg, W. H. (1915).
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891:{\displaystyle q_{Z}}
868:charge of an electron
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531:{\displaystyle b=7.4}
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36:characteristic X-rays
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2018:Photoelectric effect
1951:Characteristic X-ray
1551:relativistic effects
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263:{\displaystyle \nu }
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2038:Photodisintegration
2013:Rayleigh scattering
1992:Free-electron laser
1802:1999EJPh...20..213W
1767:1980AmJPh..48..492L
1732:1996AmJPh..64.1332R
1547:Hartree–Fock method
1423:
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1198:
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836:mass of an electron
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406:{\displaystyle b\ }
2357:History of physics
2279:X-ray reflectivity
2058:X-ray fluorescence
2023:Compton scattering
1956:High-energy X-rays
1855:2016-03-03 at the
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2259:Backscatter X-ray
2254:X-ray diffraction
2081:X-ray radiography
2053:X-ray diffraction
1946:Siegbahn notation
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305:{\displaystyle b}
285:{\displaystyle A}
176:Siegbahn notation
129:X-ray diffraction
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1916:Absorption edge
1904:Characteristics
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1843:External links
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1796:(3): 213–220.
1780:
1761:(6): 492–493.
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1674:Rechenberg, H.
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590:
587:
567:
564:
563:
562:
550:
547:
527:
524:
521:
498:
494:
486:
482:
478:
473:
466:
462:
458:
452:
448:
445:
425:
422:
399:
376:
372:
364:
360:
356:
351:
344:
340:
336:
330:
326:
323:
313:
301:
281:
271:
259:
234:
229:
225:
222:
219:
215:
210:
207:
204:
201:
163:
160:
148:
145:
136:
133:
88:
85:
73:
70:
67:
62:
15:
13:
10:
9:
6:
4:
3:
2:
2379:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2349:
2347:
2328:
2325:
2321:
2318:
2317:
2316:
2313:
2312:
2310:
2306:
2300:
2297:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2272:
2270:
2267:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2246:
2244:
2242:
2238:
2232:
2229:
2227:
2224:
2222:
2219:
2217:
2214:
2212:
2209:
2207:
2204:
2202:
2199:
2197:
2194:
2193:
2191:
2187:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2161:
2158:
2154:
2151:
2149:
2146:
2144:
2141:
2140:
2139:
2136:
2134:
2131:
2129:
2126:
2124:
2121:
2119:
2116:
2112:
2109:
2107:
2104:
2103:
2102:
2099:
2097:
2094:
2092:
2091:Tomosynthesis
2089:
2087:
2084:
2082:
2079:
2078:
2076:
2072:
2069:
2065:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2010:
2008:
2004:
1998:
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1978:
1975:
1973:
1970:
1969:
1967:
1963:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1921:Moseley's law
1919:
1917:
1914:
1912:
1909:
1908:
1906:
1902:
1898:
1897:X-ray science
1891:
1886:
1884:
1879:
1877:
1872:
1871:
1868:
1862:
1858:
1854:
1851:
1847:
1846:
1842:
1833:
1827:
1824:
1819:
1815:
1811:
1807:
1803:
1799:
1795:
1791:
1784:
1781:
1776:
1772:
1768:
1764:
1760:
1756:
1749:
1746:
1741:
1737:
1733:
1729:
1725:
1721:
1714:
1711:
1706:
1705:
1697:
1694:
1689:
1687:3-540-90642-8
1683:
1679:
1675:
1671:
1664:
1661:
1656:
1652:
1648:
1641:
1639:
1637:
1635:
1633:
1631:
1629:
1627:
1623:
1618:
1614:
1610:
1606:
1602:
1595:
1593:
1589:
1582:
1577:
1574:
1571:
1568:
1565:
1561:
1560:
1556:
1554:
1552:
1548:
1542:
1535:
1533:
1520:
1501:
1497:
1493:
1490:
1484:
1479:
1471:
1468:
1465:
1459:
1454:
1446:
1443:
1440:
1432:
1429:
1419:
1414:
1410:
1404:
1400:
1396:
1389:
1380:
1370:
1363:
1358:
1355:
1350:
1347:
1339:
1323:
1309:
1306:
1301:
1293:
1290:
1287:
1279:
1276:
1271:
1266:
1258:
1255:
1252:
1245:
1237:
1233:
1229:
1224:
1217:
1213:
1209:
1203:
1194:
1189:
1185:
1179:
1175:
1171:
1164:
1155:
1145:
1138:
1129:
1125:
1116:
1112:
1109:
1106:
1103:
1100:
1080:
1077:
1069:
1062:
1046:
1039:
1018:
1014:
1005:
978:
970:
949:
941:
925:
921:
914:
911:
908:
883:
879:
871:
869:
847:
839:
837:
815:
807:
805:
787:
783:
775:
774:
773:
759:
755:
747:
738:
734:
729:
722:
713:
709:
703:
694:
689:
685:
679:
675:
671:
664:
659:
655:
649:
640:
630:
623:
614:
610:
601:
597:
594:
591:
588:
585:
577:
573:
565:
548:
545:
525:
522:
519:
511:
496:
492:
484:
480:
476:
471:
464:
460:
456:
450:
446:
443:
423:
420:
397:
389:
374:
370:
362:
358:
354:
349:
342:
338:
334:
328:
324:
321:
314:
299:
279:
272:
257:
250:
249:
248:
232:
227:
223:
220:
217:
213:
208:
205:
202:
199:
191:
190:Moseley's Law
187:
182:
181:
177:
161:
158:
146:
144:
142:
134:
132:
130:
126:
125:Henry Moseley
122:
120:
116:
112:
111:
105:
97:
96:Henry Moseley
93:
86:
84:
71:
68:
65:
60:
50:
49:atomic number
45:
44:Henry Moseley
41:
37:
33:
32:empirical law
29:
28:Moseley's law
21:
2189:Spectroscopy
2133:Ptychography
2067:Applications
2028:Auger effect
1931:Water window
1920:
1860:
1826:
1793:
1789:
1783:
1758:
1754:
1748:
1726:(10): 1332.
1723:
1719:
1713:
1703:
1696:
1677:
1663:
1654:
1650:
1608:
1604:
1564:periodic law
1543:
1539:
1337:
1067:
1065:
569:
189:
186:approximated
185:
183:
179:
150:
138:
123:
109:
101:
27:
26:
1982:Synchrotron
436:lines, and
38:emitted by
2346:Categories
2241:Scattering
2106:Helical CT
1972:X-ray tube
1657:: 703–713.
1583:References
1562:Moseley's
576:Bohr model
566:Derivation
174:lines (in
1818:250901403
1670:Mehra, J.
1549:with the
1536:Screening
1494:⋅
1485:×
1469:−
1460:≈
1444:−
1411:ε
1348:ν
1307:×
1291:−
1272:≈
1256:−
1225:−
1186:ε
1126:−
1110:ν
1081:α
912:−
784:ε
730:−
686:ε
611:−
595:ν
549:α
497:⋅
472:−
424:α
375:⋅
350:−
258:ν
221:−
209:⋅
200:ν
162:α
135:Apparatus
66:∝
61:ν
1977:Betatron
1853:Archived
1676:(1982).
1557:See also
413:= 1 for
2320:History
2074:Imaging
1798:Bibcode
1763:Bibcode
1728:Bibcode
1541:texts.
1059:is the
866:is the
834:is the
802:is the
572:fitting
247:where:
147:Results
108:atomic
87:History
2367:X-rays
2308:Others
2269:GISAXS
1941:L-edge
1936:K-edge
1816:
1684:
1507:
1313:
772:where
561:lines.
401:
141:vacuum
119:nickel
115:cobalt
110:weight
30:is an
2299:EDXRD
2221:XANES
2216:EXAFS
2206:ARPES
2153:3DXRD
1911:X-ray
1814:S2CID
1667:e.g.
1653:. 6.
1607:. 6.
390:and
40:atoms
2284:RIXS
2274:WAXS
2264:SAXS
2175:DFXM
2143:XDCT
2128:STXM
2123:XPCI
2111:XACT
1682:ISBN
1491:2.47
1310:13.6
1015:>
538:for
512:and
292:and
102:The
2289:XRS
2231:XFH
2226:EDS
2211:AES
2201:XPS
2196:XAS
2180:DXA
2148:DCT
2096:CDI
1806:doi
1771:doi
1736:doi
1613:doi
526:7.4
2348::
2294:XS
2101:CT
1859:"
1812:.
1804:.
1794:20
1792:.
1769:.
1759:48
1757:.
1734:.
1724:64
1722:.
1672:;
1655:27
1649:.
1625:^
1609:26
1603:.
1591:^
1502:15
1498:10
192:.
180:Z.
51::
1889:e
1882:t
1875:v
1834:.
1820:.
1808::
1800::
1777:.
1773::
1765::
1742:.
1738::
1730::
1690:.
1619:.
1615::
1521:.
1518:)
1514:z
1511:H
1488:(
1480:2
1476:)
1472:1
1466:Z
1463:(
1455:2
1451:)
1447:1
1441:Z
1438:(
1433:4
1430:3
1420:2
1415:0
1405:3
1401:h
1397:8
1390:4
1385:e
1381:q
1375:e
1371:m
1364:=
1359:h
1356:E
1351:=
1338:h
1324:.
1320:V
1317:e
1302:2
1298:)
1294:1
1288:Z
1285:(
1280:4
1277:3
1267:2
1263:)
1259:1
1253:Z
1250:(
1246:)
1238:2
1234:2
1230:1
1218:2
1214:1
1210:1
1204:(
1195:2
1190:0
1180:2
1176:h
1172:8
1165:4
1160:e
1156:q
1150:e
1146:m
1139:=
1134:f
1130:E
1121:i
1117:E
1113:=
1107:h
1104:=
1101:E
1078:K
1068:b
1047:h
1037:)
1023:f
1019:n
1010:i
1006:n
983:i
979:n
954:f
950:n
926:e
922:q
918:)
915:b
909:Z
906:(
884:Z
880:q
852:e
848:q
820:e
816:m
788:0
760:,
756:)
748:2
743:i
739:n
735:1
723:2
718:f
714:n
710:1
704:(
695:2
690:0
680:2
676:h
672:8
665:2
660:Z
656:q
650:2
645:e
641:q
635:e
631:m
624:=
619:f
615:E
606:i
602:E
598:=
592:h
589:=
586:E
546:L
523:=
520:b
493:)
485:2
481:3
477:1
465:2
461:2
457:1
451:(
447:=
444:A
421:K
398:b
371:)
363:2
359:2
355:1
343:2
339:1
335:1
329:(
325:=
322:A
300:b
280:A
233:2
228:)
224:b
218:Z
214:(
206:A
203:=
159:K
72:.
69:Z
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