The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state.

(1) $\frac{1}=\left(\frac{1}{3^{2}}-\frac{1}{4^{2}}\right)$

$=\frac{7 R}{16 \times 9}$

And $\frac{1}{\lambda_{2}}=R\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)$

$=\frac{5 R}{36}$

Now $\frac{\lambda_{1}}{\lambda_{2}}=\frac{(5 R / 36)}{7 R /(16 \times 9)}=\frac{20}{7}$