Question

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

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

Answer 1

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

Time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is : $t=$distance/velocity

Distance of Bohr orbit = circumference of Bohr orbit = $2\pi r$

$t=\frac{2\pi r}{v}$

Since $mvr=\frac{nh}{2\pi }$

$v=\frac{nh}{2\pi mr}$

Thus, $t=2\pi r\times \frac{2\pi mr}{nh}$

$t=\frac{4{\pi }^{2}m{r}^2}{nh}$