The only options that apply for the set of quantum numbers in order are;
Option B; 5, 2, 1, -1/2
Option G; 4, 2, -1, -1/2
Option H; 3, 2, 0, -1/2
The missing options are;
A) 3, 2, -3, 1/2
B) 5, 2, 1, -1/2
C) 3, 3, 1, -1/2
D) 3, 2, 1, -1
E) -3, 2, 2, -1/2
F) 2, 1, 3, 1/2
G) 4, 2, -1, -1/2
H) 3, 2, 0, -1/2
The order we want to use is (n, ℓ, mℓ, ms)
Let's look at each of them;
1) n in this case can be any number from 1 to ∞. This means only positive integers excluding 0 are possible values of n.
2) ℓ is gotten from; ℓ = n - 1. This means that all values of ℓ must be less than n by 1.
3) mℓ; if l = x, then mℓ is the range of -x to +x
4) ms can only be +1/2 or -1/2
Looking at the given options, the only ones that correspond to the definitions above of n, ℓ, mℓ, ms are Options B, G & H.
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