An electron in an atom is known to be in a state with magnetic quantum number ml=−1
what is the smallest possible value of the principal quantum number n of the state?

Explanation:

It is known that the maximum value of ml is equal to the vale of l. But the minimum value of n is as follows.

                    n = l + 1

where,     n = principle quantum number

                l = azimuthal quantum number

Values of n can be 1, 2, 3, 4 and so on. Whereas the values of l can be 0, 1, 2, 3, and so on.

Also, "m" is known as magnetic quantum number whose values can be equal to -l and +l.

So, when n = 1 then l = 0 and m = 0.

When n = 2 then l = 1 and values of m will be equal to -1, 0, +1. As it is given that the magnetic quantum number ml = -1. Hence, it is only possible when n = 2.

Thus, we can conclude that the smallest possible value of the principal quantum number n of the state is 2.