Question

how many electrons in an atom can share the quantum numbers n=3, l=2 and m subscript l=2?

Answer 1

If you mean m (subscript l) is (-2,-1,0,1,2) 
its a 3d orbital so it can hold 2 electrons, however, like in an electron diagram a 3d orbital has 5 boxes can can hold 2 electrons that is how i got 10 total but if you mean just in box 2 then only 2 can share it.

Does that make sense?

Answer 2

Answer: 2 electrons.

Explanation:

The quantum numbers given are:

$n=3$

$l=2$

$m_l=2$

Paulis' exclusion principle states that only two electrons may occupy the same orbital, and that is only if each elecron has opposite spins.

The three first quantum numbers, as those given, determine an orbital. So, as Pauli's exclusion principle only two electrons in one atom can have that same set of quantum numbers.

One of the electrons will have (3, 2, 2, +1/2) and the other (3,2,2,-1/2). The four quantum numbers cannot be the same.