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Ole ed nde ene – te tr cept dding e co ue d ll no ons ton Energy (eV) -5 -10 -15 Bohr n=3- n=21 n=1- Sommerfeld ng= ng=2 ng = 1 ng=2- ng=1 1.81 x 104 eV ng=1 Dirac j=5/2,1=2 j= 3/2,1 = 1,2 j= 1/2,1 = 0,1 j= 3/2,1 = 1 j= 1/2,1 = 0,1 -j= 1/2,1=0

Ole ed nde ene – te tr cept dding e co ue d ll no ons ton Energy (eV) -5 -10 -15 Bohr n=3- n=21 n=1- Sommerfeld ng= ng=2 ng = 1 ng=2- ng=1 1.81 x 104 eV ng=1 Dirac j=5/2,1=2 j= 3/2,1 = 1,2 j= 1/2,1 = 0,1 j= 3/2,1 = 1 j= 1/2,1 = 0,1 -j= 1/2,1=0

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(a) Draw the hydrogen energy-level diagram for all states through n = 2 as in the righthand part of Figure 8-11, but with the splitting according to l also shown. (b) With arrows connecting pairs of levels, show all the transitions that are allowed by the selection
at n be able Om ted f Dende es en bit in ete tr m can except adding he co alue of hall no tions at on Dical Spectr 10-4 tion e only we ha at the confusion in the 1920s, when the modern quantum theories were being developed. The coincidence occurs because the errors made by the Sommerfeld model, in ig- noring the spin-orbit interaction and in using classical mechanics to evaluate the average energy shift due to the relativistic dependence of mass on velocity, happen to cancel for the case of the hydrogen atom. The energy levels of the hydrogen atom, as predicted by Bohr, Sommerfeld, and Dirac are shown in Figure 8-11. In order to make visible the energy-level splittings, Energy (eV) -10 -15- Bohr n = 3 n=2 n = 1. Sommerfeld ng= 3 ng = 2 ng = 1 ng=2 ng = 1 1.81 x 104 eV ng=1. Dirac j= 5/2,1 = 2 j= 3/2,1 = 1,2 j= 1/2, 10, 1 j= 3/2,1 = 1 j= 1/2,1 = 0,1 -j=1/2,1=0 Figure 8-11 The energy levels of the hydrogen atom for n = 1, 2, 3 according to Bohr, Sommerfeld, and Dirac. The displacements of the Sommerfeld and Dirac levels from those given by Bohr have been exaggerated by a factor of (1/a)2~ (137)² ~ 1.88 x 104.
Transcribed Image Text:at n be able Om ted f Dende es en bit in ete tr m can except adding he co alue of hall no tions at on Dical Spectr 10-4 tion e only we ha at the confusion in the 1920s, when the modern quantum theories were being developed. The coincidence occurs because the errors made by the Sommerfeld model, in ig- noring the spin-orbit interaction and in using classical mechanics to evaluate the average energy shift due to the relativistic dependence of mass on velocity, happen to cancel for the case of the hydrogen atom. The energy levels of the hydrogen atom, as predicted by Bohr, Sommerfeld, and Dirac are shown in Figure 8-11. In order to make visible the energy-level splittings, Energy (eV) -10 -15- Bohr n = 3 n=2 n = 1. Sommerfeld ng= 3 ng = 2 ng = 1 ng=2 ng = 1 1.81 x 104 eV ng=1. Dirac j= 5/2,1 = 2 j= 3/2,1 = 1,2 j= 1/2, 10, 1 j= 3/2,1 = 1 j= 1/2,1 = 0,1 -j=1/2,1=0 Figure 8-11 The energy levels of the hydrogen atom for n = 1, 2, 3 according to Bohr, Sommerfeld, and Dirac. The displacements of the Sommerfeld and Dirac levels from those given by Bohr have been exaggerated by a factor of (1/a)2~ (137)² ~ 1.88 x 104.
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