The frequency v of the emitted electromagnetic radiation, when a hydrogen atom de - excites from the level ${\mathrm{n}}_2$ to ${\mathrm{n}}_1$ is

$\mathrm{\upsilon }={\mathrm{RCZ}}^2\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

When the transition takes place from ${\mathrm{n}}_2=2$ to ${\mathrm{n}}_1=1$

then

$2.7\times {10}^{15}={\mathrm{RCZ}}^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)$.....(i)

When the transition takes place from ${\mathrm{n}}_2=3$ to ${\mathrm{n}}_1=1$

then let the frequency be $\mathrm{\upsilon }$.

$\therefore \mathrm{\upsilon }={\mathrm{RCZ}}^2\mathrm{ }\left(\frac{1}{1^2}-\frac{1}{3^2}\right)$.....(i)

From equation (i) and (ii), we get

$\mathrm{\upsilon }=\frac{32\times 2.7\times {10}^{15}}{27}=3.2\times {10}^{15} \mathrm{Hz}$