When the electron in the hydrogen atom jumps from 2^nd orbit to 1^st orbit, the wavelength of radiation emitted is λ. When the electrons jump from 3^rd orbit to 1^st orbit, the wavelength of emitted radiation would be

$\frac{27}{32} \lambda$

$\frac{1}{\lambda}=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$

First condition $\frac{1}{\lambda}=R\left[\frac{1}{1^2}-\frac{1}{2^2}\right] \Rightarrow R=\frac{4}{3 \lambda}$

Second condition $\frac{1}{\lambda '}=R\left[\frac{1}{1^2}-\frac{1}{3^2}\right]$

$\Rightarrow \lambda '=\frac{9}{8 R} \Rightarrow \lambda '=\frac{9}{8 \times \frac{4}{3 \lambda}}=\frac{27 \lambda}{32}$