question_answer

Find the ratio of energies of photons produced due to 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 permitted level.                

Answer:

                Energy of photon,                           \[hv\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] \[\therefore \]  \[\frac{{{(hv)}_{2\to 1}}}{{{(hv)}_{\infty \to 1}}}=\frac{\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)}{\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{\infty }^{2}}} \right)}=\frac{3}{4}=\mathbf{3:4}.\]