Question

The time of revolution of an electron around a nucleus of charge $Ze$ in nth Bohrs orbit is directly proportional to

• A. $ n $
• B. $ \frac{n^{3}}{Z^{2}} $
• C. $ \frac{n^{2}}{Z} $
• D. $ \frac{Z}{n} $

Answer 1

Answer: (B)

$r \propto \frac{n^{2}}{Z}$ and $v \propto \frac{Z}{n^{2}}$
Time period of revolution of an electron around the nucleus of charge $Ze$ is
$T=\frac{2 \pi r}{v}=2 \pi \frac{n^{2}}{Z} \cdot \frac{n}{Z}$
$\Rightarrow T \propto \frac{n^{3}}{Z^{2}}$