Each electron has its unique set of quantum numbers, which means that two electrons can share one, two, or even three quantum numbers, but never all four.
Now, you are given a
4
d
orbital and asked to find how many sets of quantum numbers can describe an electron located in such an orbital, or, in other words, how many electrons can occupy a
4
d
orbital.
So, the principal quantum number,
n
, describes the energy level on which the electron is located. In this case, you have
n
=
4
→
the electron is located on the fourth energy level
The subshell in which the electron is located is described by the angular magnetic quantum number,
l
, which for the fourth energy level takes the following values
l
=
0
→
the s-subshell
l
=
1
→
the p-subshell
l
=
2
→
the d-subshell
l
=
3
→
the f-subshell
Since you're looking for the d-subshell, you will need
l
=
2
.
The specific orbital in which the electron is located is given by the magnetic quantum number,
m
l
. For any d-subshell, the magnetic quantum number can take the values
m
l
=
{
−
2
,
−
1
,
−
0
,
+
1
,
+
2
}
Each of these five values describes one of the five d-orbitals available in a d-subshell.
