Question

In a hypothetical system a particle of mass $m$ and 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 ($h$ is Planck's constant)

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

Answer 1

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

$\frac{1}{4\pi {\epsilon }_0}\times \frac{3q^2}{r^2}=\frac{m{v}^2}{r}$(1)
$mvr=\frac{nh}{2\pi }$ (2)

By (1) and (2) and for $n$ = 1
$v=\frac{3q^2}{2{\epsilon }_{0}h}$