Question

The time of revolution of an electron around a nucleus of charge $Ze$ in $n$th Bohr's orbit is directly proportional to :

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

Answer 1

The correct option is B $\frac{n^3}{Z^2}$

$r\propto \frac{n^2}{Z}$ and $v\propto \frac{Z}{n^2}$

Time period of revolution of an electron around the nucleus of charge $Ze$ is

$T=\frac{2\pi r}{v}=2\pi \frac{n^2}{Z}\cdot \frac{n}{Z}$

$\Rightarrow T\propto \frac{n^3}{Z^2}$