4. (a) Outline how the quantum numbers n, 1 and m originate as a consequence of the solution of the Schrödinger equation for the hydrogen atom. Dis- cuss briefly what additional effects must be accounted for to explain the observed fine-structure in the energy levels. (b) If a hydrogen atomic state is written as 2P3/2 what does this tell you about it? (c) Write out, using LS notation, the states that you expect to occur for prin- cipal quantum numbers n = 2 and n = 1 in hydrogen. (d) Assuming the selection rules AL = ±1 and AJ = ±1,0 apply, how many component lines are possible for the n = 2 to n = 1 optical transition in atomic hydrogen? Illustrate your answer with a diagram showing the levels and allowed transitions. (e) How does your answer to part (d) change if the hydrogen atom is placed in a weak magnetic field?
4. (a) Outline how the quantum numbers n, 1 and m originate as a consequence of the solution of the Schrödinger equation for the hydrogen atom. Dis- cuss briefly what additional effects must be accounted for to explain the observed fine-structure in the energy levels. (b) If a hydrogen atomic state is written as 2P3/2 what does this tell you about it? (c) Write out, using LS notation, the states that you expect to occur for prin- cipal quantum numbers n = 2 and n = 1 in hydrogen. (d) Assuming the selection rules AL = ±1 and AJ = ±1,0 apply, how many component lines are possible for the n = 2 to n = 1 optical transition in atomic hydrogen? Illustrate your answer with a diagram showing the levels and allowed transitions. (e) How does your answer to part (d) change if the hydrogen atom is placed in a weak magnetic field?
Chapter10: Atomic Physics
Section: Chapter Questions
Problem 28Q
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Transcribed Image Text:4. (a) Outline how the quantum numbers n, 1 and m originate as a consequence
of the solution of the Schrödinger equation for the hydrogen atom. Dis-
cuss briefly what additional effects must be accounted for to explain the
observed fine-structure in the energy levels.
(b) If a hydrogen atomic state is written as 2P3/2 what does this tell you about
it?
(c) Write out, using LS notation, the states that you expect to occur for prin-
cipal quantum numbers n = 2 and n = 1 in hydrogen.
(d) Assuming the selection rules AL = ±1 and AJ = ±1,0 apply, how many
component lines are possible for the n = 2 to n = 1 optical transition in
atomic hydrogen? Illustrate your answer with a diagram showing the levels
and allowed transitions.
(e) How does your answer to part (d) change if the hydrogen atom is placed
in a weak magnetic field?
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