Question

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If $a_0$ is the radius of the ground state orbit, $m$ is the mass and $e$ is charge on the electron and ${\epsilon }_0$ is the vacuum permittivity, the speed of the electron is

• A. 0
• B. $\frac{e}{\sqrt{{\epsilon }_0{a}_{0}m}}$
• C. $\frac{e}{\sqrt{4\pi {\epsilon }_0{a}_{0}m}}$
• D. $\sqrt{\frac{4\pi {\epsilon }_0{a}_{0}m}{e}}$

Answer 1

Answer: (C)

Centripetal force $=$ force of attraction of nucleus on electron
$\frac{m{v}^2}{a_0}=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{e^2}{u_0^2}$
$v=\frac{e}{\sqrt{4\pi {\epsilon }_{0}m{a}_0}}$