The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to \(2^{\text {nd }}\) level is respectively

The energy of photons is given by \(E=\operatorname{Rhc}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)\)
where, \(\mathrm{R}\) is Rydberg constant, \(\mathrm{h}\) is Planck's constant and \(\mathrm{c}\) is the speed of light.
(i) Energy of photon produced from second to first energy level,
\(\mathrm{E}_{1}=\operatorname{Rhc}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)\) \(\mathrm{E}_{1}=\frac{3}{4} \mathrm{Rhc}\)
(ii) Energy of photon produced from highest energy level (i.e., \infty) to second level,
\(\begin{array}{l}
\mathrm{E}_{2}=\operatorname{Rhc}\left(\frac{1}{2^{2}}-\frac{1}{\infty}\right)=\frac{1}{4} \mathrm{Rhc} \\
\therefore \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{\frac{3}{4} \mathrm{Rhc}}{\frac{1}{4} \mathrm{Rhc}}=\frac{3}{1} \text { or } 3: 1
\end{array}\)