Explanation

(b) Radius of Bohr orbit is given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r_{n}\ =$ $\left( \frac{\varepsilon_{0}h^{2}}{\pi me^{2}} \right)n^{2}$
The quantities in the bracket are constant
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ r_{n} \propto n^{2}$
The expression gives the radius of the nth Bohr orbit
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r_{1}}{r_{2}} = \ \frac{n_{1}^{2}}{n_{2}^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{a}{r_{2}} = \ \frac{1}{3^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ r_{2} = \ 9\ a$