Separation energy of a hydrogen like ion from its third excited...

Let the separation energy of the ion be $E$. Then
$E = 13 . 6 \times {Z}^{2} \times \dfrac{1}{16}eV$
and ${E}_{H} = 13 . 6 \times \dfrac{1}{4}eV$
⇒ $\dfrac{E}{{E}_{H}} = {Z}^{2} \times \dfrac{4}{16}$
⇒ $\dfrac{2.25{E}_{H}}{{E}_{H}} = \dfrac{{Z}^{2}}{4}$

$⇒ {Z}^{2} = 9 ⇒ Z = 3$