a
\(\frac{1}{\lambda}=\frac{13.6 \mathrm{z}^2}{\mathrm{hc}}\left[\frac{1}{1^2}-\frac{1}{2^2}\right] \)   \(...(i)\)

\(\frac{1}{\lambda^{\prime}}=\frac{13.6 \mathrm{z}^2}{\mathrm{hc}}\left[\frac{1}{1^2}-\frac{1}{3^2}\right] \)  \(...(ii)\)

On dividing \((i)\) & \((ii)\)

\(\lambda^{\prime}=\frac{27}{32} \lambda\)