Final answer:
The possible values of l for an electron in the n=5 state with ml=3 are 3 and 4, as l must be at least the value of ml.
Step-by-step explanation:
If an atom has an electron in the n=5 state with ml=3, the possible values of l must be at least 3, because the magnetic quantum number ml ranges from -l to +l. Since ml is given as 3, the lowest possible value for l that can accommodate this ml value is also 3. Therefore, l must be at least 3, but it can be larger, up to one less than the principal quantum number n (which is 5 in this case). So the possible values of l are 3 and 4.
The possible values of l for an electron in the n=5 state with ml=3 can be determined by considering the rules for quantum numbers. The value of l can range from 0 to n-1. Since n=5, the possible values of l are 0, 1, 2, 3, 4. Therefore, the correct answer is a) l = 3.