The ratio of energies of photons produced due to the transition of an electron of hydrogen atom from its
i. second permitted energy level to the first level and
ii. the highest permitted energy level to the first energy level is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 : 4
By Bohr’s theory the energy of the level n of hydrogen is \( E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \), and the photon emitted in a transition carries the difference of the two level energies. The highest permitted level is \( n = \infty \), where \( E = 0 \).
\( \Delta E_{2\to1} = E_2 - E_1 = -3.4 - (-13.6) = 10.2\,\mathrm{eV} \)
\( \Delta E_{\infty\to1} = E_\infty - E_1 = 0 - (-13.6) = 13.6\,\mathrm{eV} \)
\( \displaystyle \frac{\Delta E_{2\to1}}{\Delta E_{\infty\to1}} = \frac{10.2}{13.6} = \frac{3}{4} \)