Nuclear & Particle Physics - Spectroscopic Notation

The configuration of three electrons is 1s2p3p has which of the following as the value of its maximum possible total angular momentum quantum number?

A. 7/2
B. 3
C. 5/2
D. 2
E. 3/2

(GR9277 #76)

Solution:

In Spectroscopic Notation, the total angular momentum quantum number is j = l + s, where
s = the total spin quantum number → 2n+1= multiplicity, the number of spin states
l = the orbital angular momentum quantum number

Since none of the electron sub-shells are filled, we add the individual angular momentum quantum number:
1s → l₁ = 0, s₁ = 1/2 → j₁ = 1/2
2p → l₂ = 1, s₂ = 1/2 → j₂ = 1+1/2 = 3/2
3p → l₃ = 1, s₃ = 1/2 → j₃ = 1 + 1/2 = 3/2

The maximum possible total angular momentum quantum number j = j₁ + j₂ + j₃ = 7/2

Answer: A