Answer
The maximum number of electrons possible in this atom 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.
$n=5$ means we are referring to the fourth shell. $l=3$, that means we are talking about the subshell $5f$.
Subshell $5f$ has 7 orbitals, with $m_l$ ranging from $-3$ to $3$. However, since they already gave $m_l=2$, we only consider only 1 specific orbital: $5f$ with $m_l=2$.
Two electrons in maximum can occupy an orbital. Since there is only 1 orbital here, the maximum number of electrons possible in this atom is 2.
