Answer
The electron has n= 3 and $\mathcal{l}= 2$.
Work Step by Step
The values of $m_{\mathcal{l}}$ range from $-\mathcal{l}$ to $\mathcal{l}$. Thus, for $m_{\mathcal{l}}=2$, $\mathcal{l}\geq 2$.
The possible values of $\mathcal{l}$ are from 0 to (n-1).
The lowest possible energy state is achieved for minimum n, which happens if $\mathcal{l}= 2$ and n= 3.
