1) In a hydrogen-like atom electron makes the transition from an energy level with a quantum number n to another with a quantum number (n-1). If n>>1, the frequency of radiation emitted is proportional to A) $\frac{1}{n}$ B) $\frac{1}{n^{2}}$ C) $\frac{1}{n^{4}}$ D) $\frac{1}{n^{3}}$ Answer: Option DExplanation:$ \triangle E=hv$ $v= \frac{\triangle E}{h}=k\left[\frac{1}{(n-1)^{2}}-\frac{1}{n^{2}}\right]$ $=\frac{k2n}{n^{2}(n-1)^{2}}$ $=\frac{2k}{n^{3}}\propto\frac{1}{n^{3}}$
