Question

In a hypothetical system, a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle charge $q$. Assume that Bohr's model is applicable to this system, then velocity of mass $m$ in the first orbit is

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

Answer 1

Answer: (A)

$\frac{m{v}^2}{r}=\frac{3q^2}{4\pi {\epsilon }_0{r}^2}$
$\Rightarrow mvr=\frac{3q^2}{4\pi {\epsilon }_{0}v}....$(i)
and $\frac{nh}{2\pi }=mvr....$(ii)
Using (i) and (ii) and putting $n=1$
$\frac{h}{2\pi }=\frac{3q^2}{4\pi {\epsilon }_{0}v}$
$\Rightarrow v=\frac{3q^2}{2{\epsilon }_{0}h}$