If an atom has an electron in the n = 4 state with ml = 2, what are the possible values of l?

The possible values of l are 2 and 3

Explanation:

Each electrons have four quantum numbers:

n: the principal quantum number, which value matches with the energy level of the electron. l: the secondary quantum number, which value can be from 0 to n-1 m: the magnetic number, which value can be from - l to l sp: the spin number which value can be - 1/2 or + 1/2

In this case, n=4 so the values of l are:

l=0, 1, 2, 3

Now, if:

l=0 the value of m is m=0 l=1 the values of m are m = - 1, 0, 1 l=2 the values of m are m = - 2, - 1, 0, 1, 2 l=3 the values of m are m = - 3, - 2, - 1, 0, 1, 2, 3

Being all that said, l can be either equal to 2 or 3