Electron Orbitals

Question

A single electron in an orbital has quantum numbers n = 3, ℓ = 0, mℓ = 0, ms =-½. What are the quantum numbers for the next electron added to this orbital?

A) n = 3, ℓ =1, mℓ = 0, ms = +½

B) n = 3, ℓ = 0, mℓ = 0, ms = -½

C) n = 3, ℓ = 1, mℓ = 0, ms = -½

D) n = 3, ℓ = 0, mℓ = 0, ms = +½

E) n = 3, ℓ = 1, mℓ = 1, ms = +½

Answer 1

Chemistry classes somewhat arbitrarily build up the electron configurations from lower values of quantum numbers to higher - it's actually arbitrary when choosing between equivalent energy sets of quantum number. Given this convention an electron will occupy s = -1/2 before 1/2 and m= -1 before m= 0 and 1.

Based on the assumption of this convention, you have one electron in the 3s orbital. The next electron will fill that orbital and have the same QNs except s = 1/2. (D)

If you have the (bizarre, but possible) convention that the electrons populate the degenerate quantum levels from high QN to low, the -1/2 spin would mean this is the second electron in the 3s and the next would have the quantum address n=1, l=1, m=1, s=1/2 (unfortunately, E)

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