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Which of the following is not permissible arrangement of electrons in an atom?

1. n = 5, l = 3, mₗ = 0, s = +1/2
2. n = 3, l = 2, mₗ = -3, s = 1/2
3. n = 3, l = 2, mₗ = -3, s = -1/2
4. n = 4, l = 0, mₗ = 0, s = -1/2

Correct answer: n = 3, l = 2, mₗ = -3, s = 1/2

Solution

The magnetic quantum number (mₗ) must lie between -l and +l, inclusive. For n = 3 and l = 2, mₗ cannot be -3 as it exceeds the allowed range (-2 to +2).

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