d
Second excited state \(\rightarrow\) first excited state

\(n =3 \rightarrow n =2\)

\(\frac{ hc }{\lambda_0}=13.6\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \ldots \ldots \text { (i) }\)

Third excited state \(\rightarrow\) second orbit

\(n =4 \rightarrow n =2\)

\(\frac{ hc }{\left(20 \lambda_0 / x \right)}=13.6\left(\frac{1}{2^2}-\frac{1}{4^2}\right) \text {. }\)

\((ii)\) \(\div\) \((i)\)

\(\frac{x}{20}=\frac{\frac{1}{2^2}-\frac{1}{4^2}}{\frac{1}{2^2}-\frac{1}{3^2}}\)

\(x=27\)