Problem page an electron in an atom is known to be in a state with magnetic quantum number =ml−2 . what is the smallest possible value of the principal quantum number n of the state?

The smallest possible value of the principal quantum number n of the state is n = 3

The four sets of quantum numbers that describe the position of an electron in an atom are;

For an atom having magnetic quantum number ml = -2, the smallest possible value of the  principal quantum number n of the state is n= 3 because a magnetic quantum number ml = -2 corresponds to a d orbital.

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n = 3. The principal quantum number must be at least 3 to have a magnetic quantum number ml = -2

The rules are:

•n > 0

•l < n

•|ml| ≤ l

Thus, if ml = -2, l ≥ 2.

If l ≥ 2 and n > l, the allowed values of n are 3, 4, 5, etc.

The smallest allowed value of n is n  = 3.