Question:
A particular hydrogen like ion emits radiation of frequency $2.92 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $\mathrm{n}=3$ to $\mathrm{n}=1$. The frequency in $\mathrm{Hz}$ of radiation emitted in transition from $\mathrm{n}=2$ to $\mathrm{n}=1$ will be:
Correct Option: , 4
Solution:
$\mathrm{nf}_{1}=\mathrm{k}\left(\frac{1}{1}-\frac{1}{3^{2}}\right)$
$\mathrm{nf}_{2}=\mathrm{k}\left(1-\frac{1}{2^{2}}\right)$
$\frac{f_{1}}{f_{2}}=\frac{8 / 9}{3 / 4} \Rightarrow f_{2}=2.46 \times 10^{15}$
Option (4)