Question

In the Bohr's 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 ${ϵ}_0$ is the vacuum permittivity, the speed of the electron is

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

Answer 1

The correct option is C $\frac{e}{\sqrt{4\pi {ϵ}_0{a}_{0}m}}$

Centripetal force $=$ Force of attraction of nucleus on electron

$\frac{m{v}^2}{a_0}=\frac{1}{4\pi {ϵ}_0}\frac{e^2}{a_0^2}$

$\Rightarrow v=\frac{e}{\sqrt{4\pi {ϵ}_{0}m{a}_0}}$