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Find the maximum number of electrons in the third shell (n = 3) that can have spin quantum number ms = -1/2.

1. 5
2. 9
3. 18
4. 8

Correct answer: 9

Solution

For the n = 3 shell, the subshells are 3s, 3p, and 3d. 3s: 1 orbital -> maximum 1 electron with ms = -1/2 3p: 3 orbitals -> maximum 3 electrons with ms = -1/2 3d: 5 orbitals -> maximum 5 electrons with ms = -1/2 Total = 1 + 3 + 5 = 9 electrons with ms = -1/2. This equals half of 2n² = 18 total electrons.

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