Let T _ 1 and T _ 2 be the energy of an electron in the first and...

Given ${T}_{1} ⇒$ Energy of ${1}^{st}$ excited state

For ${T}_{1} ⇒ n = 2$

For ${T}_{2} ⇒ n = 3$

We know, Energy $∝ \dfrac{1}{{n}^{2}}$

$∴ \dfrac{{T}_{1}}{{T}_{2}} = \dfrac{{3}^{2}}{{2}^{2}} = \dfrac{9}{4}$