Final answer:
For the quantum numbers n = 3, l = 2, ten electrons can fit because each of the five possible ml values (-2, -1, 0, +1, +2) can pair with two different spin states (+1/2 or -1/2), leading to 10 unique sets of quantum numbers.
Step-by-step explanation:
The question is asking how many electrons in an atom can have the quantum numbers n = 3, l = 2. According to the rules for quantum numbers, for any given value of n, the azimuthal quantum number l can range from 0 to n-1. For l = 2, which designates the d-subshell, the magnetic quantum number ml can have five values: -2, -1, 0, +1, +2. Each of these can be paired with two spin states, s = +1/2 or -1/2, given by the spin quantum number ms. This means there are two possible values of ms for each ml, totaling 10 electrons.