Question

In Bohr’s model of hydrogen atom, for dynamic stable orbit, relation between orbit radius $\left(r\right)$ and speed of electron $\left(v\right)$ is

$[e-$ charge on an electron, $m-$ mass of an electron$]$

• A. $r=\frac{e^2}{2\pi {ϵ}_{0}m{v}^2}$
• B. $r=\frac{3e^2}{4\pi {ϵ}_{0}m{v}^2}$
• C. $r=\frac{e^2}{8\pi {ϵ}_{0}m{v}^2}$
• D. $r=\frac{e^2}{4\pi {ϵ}_{0}m{v}^2}$

Answer 1

The correct option is D $r=\frac{e^2}{4\pi {ϵ}_{0}m{v}^2}$

For dynamic stable orbit, electrostatic force will provide the necessary centripetal acceleration.

$\therefore F_e=m{a}_c$

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

$\Rightarrow r=\frac{e^2}{4\pi {ϵ}_{0}m{v}^2}$