Answer
$n = 3$, $l = 1$ also known as the $3p$ state
Work Step by Step
The hydrogen atom's energy is given by:
$$E = \frac{-13.6 eV}{n^2}$$
while the angular momentum is given by:
$$L = \sqrt{l(l+1)\hbar}$$
Therefore, according to the problem if, $E = \frac{-13.60}{9} eV$ and $L = \sqrt{2}\hbar$
Then, $n$ must be equal to $3$ and $l$ must be equal to $1$.
