Physics - Modern Physics Question with Solution | TestHub

where subscripts $h$ and $g$ denotes higher energy state and ground state. Orbital velocity of electron in the $n^{\text{th }}$ orbit is $v_n=\frac{e^2}{2{\epsilon }_{0}nh}$ or $v_n\propto \frac{1}{n}$
Equating eqns. (i) and (ii), we get $n=3$ Radius of $n^{\text{th }}$ orbit is $r_n=\frac{n^2{h}^2{\epsilon }_0}{\pi e^2{m}^2}$ or $r_n\propto n^2$ $\begin{array}{rl}\therefore \frac{r_3}{r_1}& =\frac{(3{)}^2}{(1{)}^2}=9\\ r_3& =9r_1=9R\left(\because r_1=R(\text{ Given })\right)\end{array}$