When the electron in a hydrogen atom jumps from the second orbit to the first orbit, the wavelength of the radiation emitted is λ. When the electron jumps from the third to the first orbit, the wavelength of the radiation emitted is

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

$\frac{1}{\lambda} = R(\frac{1}{1^2} - \frac{1}{2^2}) = \frac{3R}{4}$

$\frac{1}{\lambda'}= R(\frac{1}{1^2} - \frac{1}{3^2}) = \frac{8R}{9}$

$\frac{\lambda'}{\lambda} = \frac{27}{32} \Rightarrow \lambda'= \frac{27\lambda}{32}$