\(\frac{1}{\lambda_{1}}= R z^{2}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)\)

\(\frac{1}{\lambda_{1}}= R z^{2} \frac{5}{36}\) ........\((i)\)

For \(3^{\text {rd }}\) line

\(\frac{1}{\lambda_{3}}= Rz ^{2}\left(\frac{1}{2^{2}}-\frac{1}{5^{2}}\right)\)

\(\frac{1}{\lambda_{3}}= Rz ^{2} \frac{21}{100}\) \(.........(ii)\)

(ii) \(+( i )\)

\(\frac{\lambda_{1}}{\lambda_{3}}=\frac{21}{100} \times \frac{36}{5}=1.512=15.12 \times 10^{-1}\)

\(x \approx 15\)