Q 12-12-106JEE MainJEE Main 2020 (2 Sep, Shift 2)Medium
In a hydrogen atom the electron makes a transition from $(n+1)^{\text{th}}$ level to the $n^{\text{th}}$ level. If $n \gg 1$, the frequency of radiation emitted is proportional to:
Answer: (B) $\dfrac{1}{n^{3}}$
$$\nu \propto \frac{1}{n^{2}} - \frac{1}{(n+1)^{2}} = \frac{2n+1}{n^{2}(n+1)^{2}} \approx \frac{2n}{n^{4}} = \frac{2}{n^{3}}$$
So $\nu \propto 1/n^{3}$ for large $n$.
Solution by Sreeraj P, M.Sc Physics