16. Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit cou- pling). The energy levels can be written as 1 2 Enj = — — — mec²2012 | [1 n 3 1+ n2 n2 +1/2 ¾)] where a = : e²/(4ɛ。ħc) ≈ 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level according to angular momentum & 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.
16. Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit cou- pling). The energy levels can be written as 1 2 Enj = — — — mec²2012 | [1 n 3 1+ n2 n2 +1/2 ¾)] where a = : e²/(4ɛ。ħc) ≈ 1/137 is the fine structure constant. (a) How many different energy levels are associated with the n=2 state? Label each energy level according to angular momentum & 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.
Question
![16. Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit cou-
pling). The energy levels can be written as
1
2
Enj = — — — mec²2012 | [1
n
3
1+
n2
n2 +1/2
¾)]
where a =
: e²/(4ɛ。ħc) ≈ 1/137 is the fine structure constant.
(a) How many different energy levels are associated with the n=2 state? Label each energy level according to
angular momentum & 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18ff836d-3cc8-4a2b-b721-7f7a69fbe250%2F5ec30582-581a-44de-9755-acee90a4c19c%2Frznqfnj_processed.png&w=3840&q=75)
Transcribed Image Text:16. Consider the energy levels of hydrogen which include the fine structure correction (relativistic + spin-orbit cou-
pling). The energy levels can be written as
1
2
Enj = — — — mec²2012 | [1
n
3
1+
n2
n2 +1/2
¾)]
where a =
: e²/(4ɛ。ħc) ≈ 1/137 is the fine structure constant.
(a) How many different energy levels are associated with the n=2 state? Label each energy level according to
angular momentum & 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.
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