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Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit coupling). The energy levels can be written as 1 n Enj 1+ n2 n2 = - + 1/2 4 where a = e/(4Te0hc) 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level accord- ing to angular momentum l and total angular momentum j using the notation "nL;" and the letters S, P, D for l = 0, 1 and 2 respectively, i.e. the n = 2, l = 1, j = 3/2 state is written as 2P3/2. (b) How many lines there will be in the transition from the n=3 state → n=2 state? Label the transition lines using the notation of part (a) above. Assume the transition obeys the selection rule Al = ±1. (c) Evaluate the wavelength of the emitted photons is (b) above expressing them as Ao + AX, where 2 a² (0)- 기(0) hc/(E" – E") is the wavelength associated with the Bohr energies: E -13.6금 eV. do = %3D n2

Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit coupling). The energy levels can be written as 1 n Enj 1+ n2 n2 = - + 1/2 4 where a = e/(4Te0hc) 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level accord- ing to angular momentum l and total angular momentum j using the notation "nL;" and the letters S, P, D for l = 0, 1 and 2 respectively, i.e. the n = 2, l = 1, j = 3/2 state is written as 2P3/2. (b) How many lines there will be in the transition from the n=3 state → n=2 state? Label the transition lines using the notation of part (a) above. Assume the transition obeys the selection rule Al = ±1. (c) Evaluate the wavelength of the emitted photons is (b) above expressing them as Ao + AX, where 2 a² (0)- 기(0) hc/(E" – E") is the wavelength associated with the Bohr energies: E -13.6금 eV. do = %3D n2

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Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit coupling). The energy levels can be written as 2 1+ n2 1 En.j 2 n2 + 1/2 where a = e2/(4Te0ħc) 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level accord- ing to angular momentum l and total angular momentum j using the notation “nL;" and the letters S, P, D for l = 0, 1 and 2 respectively, i.e. the n = 2, l = 1, j = 3/2 state is written as 2P3/2. (b) How many lines there will be in the transition from the n=3 state → n=2 state? Label the transition lines using the notation of part (a) above. Assume the transition obeys the selection rule Al = ±1. (c) Evaluate the wavelength of the emitted photons is (b) above expressing them as Ao + AX, where do = hc/(E – E") is the wavelength associated with the Bohr energies: E = -}mec² -13.6금 eV. „(0)
Transcribed Image Text:Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit coupling). The energy levels can be written as 2 1+ n2 1 En.j 2 n2 + 1/2 where a = e2/(4Te0ħc) 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level accord- ing to angular momentum l and total angular momentum j using the notation “nL;" and the letters S, P, D for l = 0, 1 and 2 respectively, i.e. the n = 2, l = 1, j = 3/2 state is written as 2P3/2. (b) How many lines there will be in the transition from the n=3 state → n=2 state? Label the transition lines using the notation of part (a) above. Assume the transition obeys the selection rule Al = ±1. (c) Evaluate the wavelength of the emitted photons is (b) above expressing them as Ao + AX, where do = hc/(E – E") is the wavelength associated with the Bohr energies: E = -}mec² -13.6금 eV. „(0)
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