How many electrons can possess this set of quantum numbers: principal quantum number n = 4, magnetic quantum number mℓ = - 1?

6 electrons

Explanation:

To solve this question lets determine the possible quantum numbers for the principal quantum number n = 4.

For the quantum number l which describes the shape of the orbital, we have the possible values : 0 to n-1.

Thus, for n = 4 the l can assume the values 0, 1, 2, 3 (4 possible shapes)

For the angular quantum number, ml, which tell us the orientation in space, we have the values - l to + l.

So lets determine the number of orbials which can have the values - l for n=4

l = 0 ml = 0

l = 1 ml = - 1,0,1

l = 2 ml = - 2, - 1, 0, 1, 2

l = 3 ml = - 3,-2,-1,0,1,2,3

So we have three orbital with ml = - 1 and from Pauli's exclusion principle we can have up two electrons in each orbital. Thus for n = 4 we can have up to 6 electrons with ml = - 1