Question

Transition of first Balmer line

$$\begin{matrix} & & n_{1} = 2;n_{2} = 3 \\ & \Delta E = x = 13.6(1)^{2}\left\lbrack \frac{1}{2^{2}} - \frac{1}{3^{2}} \right\rbrack & \text{……………}\text{.}\text{(i)} \end{matrix}$$

Transition of $2\ ^{\text{nd~}}$ Balmer line

$$\begin{matrix} & & n_{1} = 2;n_{2} = 4 \\ & \Delta E = 13.6(1)^{2}\left\lbrack \frac{1}{2^{2}} - \frac{1}{4^{2}} \right\rbrack\ldots\ldots\ldots\ldots\ldots.. & \text{(ii)} \end{matrix}$$

Divide Eq. (ii) by eq. (i)

$${\frac{\Delta E}{x} = \frac{\frac{1}{4} - \frac{1}{16}}{\frac{1}{4} - \frac{1}{9}} }{\frac{\Delta E}{x} = \frac{\frac{3}{16}}{\frac{5}{36}} }{\frac{\Delta E}{x} = \frac{27}{20} }$$$\Delta E = 1.35x$.