Physics - Modern Physics Question with Solution | TestHub

The velocity of an electron in the ground state of a hydrogen atom can be derived from Bohr's postulates. According to Bohr's model, the angular momentum is quantized:

$mvr=n\frac{h}{2\pi }$.

For the ground state, $n=1$, so $v=\frac{h}{2\pi mr}$.

Also, the electrostatic force provides the centripetal force: $\frac{e^2}{4\pi {ϵ}_0{r}^2}=\frac{m{v}^2}{r}$.

Solving for $v$ using $v=\frac{h}{2\pi mr}$ gives $v=\frac{e^2}{2{ϵ}_{0}h}$. Therefore, option D is correct.