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Question
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
- n = 0, l = 0, ml = 0, ms = + ½
- n = 1, l = 0, ml = 0, ms = – ½
- n = 1, l = 1, ml = 0, ms = + ½
- n = 2, l = 1, ml = 0, ms = – ½
- n = 3, l = 3, ml = –3, ms = + ½
- n = 3, l = 1, ml = 0, ms = + ½
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Solution
a. n = 0, l = 0, mₗ = 0, mₛ = +½
Not possible, because n cannot be 0.
b. n = 1, l = 0, mₗ = 0, mₛ = –½
Possible, because all values follow rules (l < n, mₗ = 0, valid mₛ).
c. n = 1, l = 1, mₗ = 0, mₛ = +½
Not possible, because for n = 1, l must be 0 (since l = 0 to n – 1).
d. n = 2, l = 1, mₗ = 0, mₛ = –½
Possible, all values valid.
e. n = 3, l = 3, mₗ = –3, mₛ = +½
Not possible, because l cannot be equal to n; it must be less than n.
f. n = 3, l = 1, mₗ = 0, mₛ = +½
Possible, all values valid.
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