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For which one of the following sets of four quantum numbers, an electron will have the highest energy?

1. n = 3, l = 2, m = 1, s = 1/2
2. n = 4, l = 2, m = −1, s = 1/2
3. n = 4, l = 1, m = 0, s = −1/2
4. n = 5, l = 0, m = 0, s = −1/2

Correct answer: n = 4, l = 2, m = −1, s = 1/2

Solution

The energy of an electron is determined by the principal quantum number (n) and the azimuthal quantum number (l). The higher the value of (n + l), the higher the energy. If (n + l) is the same, the electron with the higher n has more energy. Option B has n = 4 and l = 2, giving (n + l) = 6, which is the highest among the options.

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