Question

In the $n$ th orbit of hydrogen atom, ratio of its radius and de-Broglie wavelength associated with it, is:

• A. $ \frac{1}{2\pi n} $
• B. $ \frac{1}{2\pi {{n}^{2}}} $
• C. $ \frac{n}{2\pi } $
• D. $ \frac{{{n}^{2}}}{2\pi } $

Answer 1

Answer: (C)

The velocity of electron in $n$th orbit is given by
$v=\frac{n h}{2 \pi m r_{n}}$
Also, $ \lambda=\frac{h}{p}=\frac{h}{m v}$
From eqs. (1) and (2), we have
$\lambda =\frac{h}{m \frac{n h}{2 \pi m r_{n}}}$
$=\frac{2 \pi r_{n}}{n} $
$\therefore \frac{r_{n}}{\lambda} =\frac{n}{2 \pi}$