question_answer

Calculate the ratio of energies of photons produced due to transition of electron of hydrogen atom from its, (ii) second permitted energy level to the first level, and (ii) highest permitted energy level to the second permitted level. 

Answer:

                \[{{v}_{1}}\propto \left[ \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right]\]                 or            \[{{v}_{1}}\propto \frac{3}{4}\]                 (ii) \[{{v}_{2}}\propto \left[ \frac{1}{{{2}^{2}}}-\frac{1}{{{\infty }^{2}}} \right]\]                 or            \[{{v}_{2}}\propto \frac{1}{4}\]                 \[\therefore \]  \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{v}_{1}}}{{{v}_{2}}}\] \[=\frac{3}{4}\times \frac{4}{1}=3:1.\]