The quantum numbers n and l represent different properties of an electron's orbital in an atom. The quantum number n indicates the principal energy level or shell, while the quantum number l represents the azimuthal or orbital angular momentum quantum number.
For a given value of n, the range of possible values for l is from 0 to (n - 1). In this case, n = 3, so the possible values of l are 0, 1, and 2.
The maximum number of electrons that can have a specific combination of n and l is given by the formula: 2(2l + 1). Therefore, for l = 2, the maximum number of electrons is:
2(2 * 2 + 1) = 2(4 + 1) = 2 * 5 = 10
Thus, in an atom where n = 3 and l = 2, a maximum of 10 electrons can have these quantum numbers.