If the radius of $2^{nd}$ Bohr orbit of hydrogen atom is $r_2$, then the radius of the third Bohr orbit will be:

The correct option is C $\frac{9}{4}{r}_2$
We know,
$r_n=52.9\frac{n^2{r}_o}{Z}$
where $r_n$ is the radius of the $n^{th}$ orbit.
Z = 1 for hydrogen, the ratio of radius of $2^{nd}to{3}^{rd}$ orbit will be
$\frac{r_2}{r_3}=\frac{2^2}{3^2}$
$\frac{r_2}{r_3}=\frac{4}{9}$
$\Rightarrow r_3=\frac{9}{4}{r}_2$