Quantum Mechanics - Spectroscopic Notation

A 3p electron is found in the ³P_3/2 energy level of a hydrogen atom. Which of the following is true about the electron in this state?

A. It is allowed to make an electric dipole transition to the ²S_1/2 level
B. It is allowed to make an electric dipole transition to the ²P_1/2 level
C. It has quantum numbers l = 3, j = 3/2, s = 1/2
D. It has quantum numbers n = 3, j = l, s = 3/2
E. It has exactly the same energy as it would in the ³D_3/2 level

(GR9677 #41)

Solution:

Spectroscopic notation: N^2s+1 L_j=l+s

For ³P_3/2  : 

P → l = 1
j = 3/2

→ (C) and (D) are FALSE

Selection rules (for electron transition):

1.	Principal quantum number	:	∆n = anything
2.	Orbital angular momentum	:	∆l = ±1
3.	Magnetic quantum number	:	∆ml = 0, ±1
4.	Spin	:	∆s = 0
5.	Total angular momentum	:	∆j = 0, ±1, but j = 0 ↛j = 0

(A) TRUE
Transition for ∆l = 0 is allowed.

(B) FALSE
Transition for ∆l = 0 is not allowed.

(E) FALSE
Electron can not move to different energy level (P to D) while maintaining the same energy.

Answer: A