Answer
The maximum number of electrons in this atom in this situation is 2.
Work Step by Step
*NOTES TO REMEMBER:
- The maximum number of electrons which can occupy an orbital is 2.
- The number of orbitals in a subshell depends on the type of subshells:
+) Subshell $s$: $l=0$, so $m_l=0$. Therefore, 1 orbital.
+) Subshell $p$: $l=1$, so $m_l=-1,0,1$. Therefore, 3 orbitals.
+) Subshell $d$: $l=2$, so $m_l=-2,-1,0,1,2$. Therefore, 5 orbitals.
+) Subshell $f$: $l=3$, so $m_l=-3,-2,-1,0,1,2,3$. Therefore, 7 orbitals.
$n=3$ means the orbital is in the third shell. Therefore, $l=0,1$ or $2$.
$m_l=-2$. Since $l\ge|m_l|$, we have $l\ge2$
Overall, $l$ must be equal to $2$, the subshell is $3d$.
There are 5 possible orbitals with $l=2$, corresponding with 5 values of $m_l$. However, since here $m_l$ is given to be $-2$, which means there is only one possible orbital here: $3d$ with $m_l=-2$.
1 orbital can occupy 2 electrons in maximum. Therefore, only 2 electrons in maximum can be in this atom.
