Electron in the n = 4 state with ml = 2, what are the possible values of l?

l = 2, 3

Explanation:

Given the principal quantum number, n, we have that the angular momentum number from 0 to n-1, and the magnetic quantum number can have the values from - l to + l.

For n = 4 (principal quantum number), we have that l, angular quantum number, can have the values 0, 1, 2, 3, and for each l value ml, magnetic quantum number, can have the values from - l to + l:

ml (for l=0) : 1 (s orbital)

ml (for l = 1) : - 1, 0, + 1 (p orbitals)

ml (for l = 2) : - 2,-1,0,+1,+2 (d orbitals)

ml (for l = 3) : - 3,-2,-1,0+,1,+2 (f orbitals)

So we see that the possible values of l for ml = 2 are l = 2 and l=3