Question

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is :

• A. $\frac{4m^2\pi r^2}{n^2{h}^2}$
• B. $\frac{n^2{h}^2}{4m{r}^2}$
• C. $\frac{4{\pi }^{2}m{r}^2}{nh}$
• D. $\frac{nh}{4{\pi }^{2}m{r}^2}$

Answer 1

The correct option is C $\frac{4{\pi }^{2}m{r}^2}{nh}$

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is $\frac{4{\pi }^{2}m{r}^2}{nh}$
According to Bohr's model, the angular momentum (mvr) is an integral multiple of $\frac{h}{2\pi }$
$mvr=\frac{nh}{2\pi r}$
$v=\frac{nh}{2\pi mr}...\left(i\right)$
and $T=\frac{2\pi r}{v}=\frac{2\pi r\times 2\pi rm}{nh}=\frac{4{\pi }^{2}m{r}^2}{nh}$