where subscripts $h$ and $g$ denotes higher energy state and ground state. Orbital velocity of electron in the $n^{\text {th }}$ orbit is
$v_n=\frac{e^2}{2 \varepsilon_0 n h} \quad$ or $\quad v_n \propto \frac{1}{n}$

Equating eqns. (i) and (ii), we get $n=3$
Radius of $n^{\text {th }}$ orbit is $r_n=\frac{n^2 h^2 \varepsilon_0}{\pi e^2 m^2}$ or $r_n \propto n^2$
$\begin{aligned} \therefore \quad \frac{r_3}{r_1} & =\frac{(3)^2}{(1)^2}=9 \\ r_3 & =9 r_1=9 R \quad\left(\because r_1=R(\text { Given })\right)\end{aligned}$