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Consider the following sets of quantum numbers: (i) n = 3, l = 0, mₗ = 0, s = +1/2 (ii) n = 2, l = 2, mₗ = 1, s = +1/2 (iii) n = 4, l = 3, mₗ = -2, s = -1/2 (iv) n = 1, l = 0, mₗ = -1, s = -1/2 (v) n = 3, l = 2, mₗ = 3, s = +1/2 Which of the following sets of quantum number is not possible?

1. (i), (ii), (iii) and (iv)
2. (ii), (iv) and (v)
3. (i) and (iii)
4. (iii), (iii) and (iv)

Correct answer: (ii), (iv) and (v)

Solution

Set (ii) is invalid because l cannot be 2 for n=2 (l ranges from 0 to n-1). Set (iv) is invalid because mₗ cannot be -1 for l=0 (mₗ ranges from -l to +l). Set (v) is invalid because mₗ cannot be 3 for l=2. Thus, (ii), (iv), and (v) are not possible.

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