Which level of the single ionized carbon has the same energy as the...

Energy of $H$ -atom is $E = - 13 . 6{Z}^{2} / {n}^{2}$ for $H$-atom $Z = 1$ and for ground state, $n = 1$

$⇒ E = - 13 . 6 \times \dfrac{{1}^{2}}{{1}^{2}} = - 13 . 6eV$

Now for carbon atom (single ionised), $Z = 6$

$E = - 13 . 6\dfrac{{Z}^{2}}{{n}^{2}} = - 13 . 6$ (given)

$⇒ {n}^{2} = {6}^{2} ⇒ n = 6$