How many electrons can have the following quantum numbers in an atom: n =
3,1 = 2? Explain.

10 e
−

Explanation:
The idea here is that you must use the value of the angular momentum quantum number, m1 which tells you the energy subshell in which an electron resides, to find the possible values of the magnetic quantum number.

The number of values that the magnetic quantum number can take tells you the number of orbitals that are present in
So, you know that the magnetic quantum number depends on the value of the angular momentum quantum numberml={−l,−(1−1),...,−1,−0,+1,...,+(l−1),+l}
In your case, you have
l=2
, which is an accepted value for the angular momentum quantum number given the fact that the principal quantum number,
n
, is equal to
3
, so you can say thatml={−2,−1,−0,+1,+2}

This tells you that the
d
subshell, which is denoted by
l=2
, holds a total of 5 orbitals.
Since each orbital can hold a maximum of 2 electrons, one having spin-up and one having spin-down, you can say that you have 5 orbitals⋅2 e−1 orbital=10 e−

Therefore, a maximum number of
10
electrons can share these two quantum numbers in an atom.
n=3
,
l=2

These electrons are located on the third energy level, in the
3d
hope this helps