Question

An electron in the ground state of hydrogen atom is revolving in anticlockwise direction in circular orbit of radius $R$. The orbital magnetic dipole moment of the electron will be

• A. $\frac{eh}{\pi m}$
• B. $\frac{eh}{4\pi m}$
• C. $\frac{e{h}^2}{4\pi m}$
• D. $\frac{e^{2}h}{4\pi m}$

Answer 1

Answer: (B)

According to Bohrs theory,
$mvr=n\frac{h}{2\pi }=\frac{h}{2\pi }(\because n=1)$
$\therefore v=\frac{h}{2\pi mr}$
We know that rate of flow of charge is current.
$\therefore I=e(\frac{v}{2\pi r})=\frac{ev}{2\pi r}$
$=\frac{e}{2\pi r}\times \frac{h}{2\pi mr}$
$=\frac{eh}{4{\pi }^{2}m{r}^2}$
Magnetic dipole moment $=IA$
$\therefore M=\frac{eh}{4{\pi }^{2}m{r}^2}\times \pi r^2$
$=\frac{eh}{4\pi m}$