Explanation

(a) For $n$th Bohr orbit,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r\ =$ $\frac{\varepsilon_{0}n^{2}h^{2}}{\pi mZe^{2}}$
de-Broglie wavelength
$\lambda = \frac{h}{mv}$
Ratio of both $r$ and $\lambda$, we have
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r}{\lambda}$ = $\frac{\varepsilon_{0}n^{2}h^{2}}{\pi mZe^{2}} \times \frac{mv}{h}$
=$\frac{\varepsilon_{0}n^{2}hv}{\pi Ze^{2}}$
But $v =$ $\frac{{Ze}^{2}}{2h\varepsilon_{0}n}$ for $n$th orbit
Hence, $\frac{r}{\lambda} = \frac{n}{2\pi}$