Final answer:
For an atom with n = 3 and l = 2, there are 10 possible sets of quantum numbers, and thus 10 electrons can occupy this subshell.
Step-by-step explanation:
The number of electrons in an atom that can have the quantum numbers n = 3, l = 2 is determined by the rules of quantum mechanics, which tell us that for a given set of n and l values, the magnetic quantum number ml can have values ranging from -l to +l, including zero.
That said, with l = 2, the possible values of ml are -2, -1, 0, 1, and 2. Each of these can be paired with two possible values of the spin quantum number ms, which can be either +1/2 or -1/2. Therefore, the number of electrons that can have these quantum numbers is the number of possible ml values times two, for the two possible spins, giving us 5 ml values × 2 spins per ml = 10 electrons.