Question

The wavelengths and frequency of radiation of photons in transitions 1, 2 and 3 for hydrogen like atom are $\lambda_{1}, \lambda_{2}, \lambda_{3}$ and $v_{1}, v_{2}, v_{3}$ respectively. Calculate the value of $\lambda_{3}$. (Vide fig.)

Answer 1

SOLUTION : $E_{3}=E_{1}+E_{2}$ (by definition)

Here

$h v_{3}=h v_{1}+h v_{2}$

Further $\frac{h c}{\lambda_{3}}=\frac{h c}{\lambda_{1}}+\frac{h c}{\lambda_{2}}$

or, $\quad \frac{1}{\lambda_{3}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}$

$\therefore \quad \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$