Question

In a hypothetical system of particles a mass $m$ with charge $-3q$ is moving around a very heavy particle having charge q. Assuming Bohr’s model to be true to this system, the orbital velocity of mass $m$ when it is nearest to heavy particle is

• A. $\frac{3q^2}{2{\epsilon }_{0}h}$
• B. $\frac{3q^2}{4{\epsilon }_{0}h}$
• C. $\frac{3q}{2{\epsilon }_{0}h}$
• D. $\frac{4q}{2{\epsilon }_{0}h}$

Answer 1

The correct option is A $\frac{3q^2}{2{\epsilon }_{0}h}$

As we know that centripetal force is provided by Coulomb's force, so
$\frac{m{v}^2}{r}=\frac{3q^3}{4\pi {ϵ}_0{r}^2}$
$mvr=\frac{3q^2}{4\pi {ϵ}_{0}v}$.......(i)
and we know that
$\frac{nh}{2\pi }=mvr$......(ii)

Using Bohr's (i) and (ii) and putting $n=1$
$\frac{h}{2\pi }=\frac{3q^2}{4\pi {ϵ}_{0}v}$
$\therefore v=\frac{3q^2}{2\pi {ϵ}_{0}h}$