Question

In a hypothetical system, a particle of mass $m$ and charge $-3 q$ 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. $\frac{3 q^2}{2 \varepsilon_0 h}$
• B. $\frac{3 q^2}{4 \varepsilon_0 h}$
• C. $\frac{3 q}{2 \pi \varepsilon_0 h }$
• D. $\frac{3 q}{4 \pi \varepsilon_0 h}$

Answer 1

Answer: (A)

$\frac{ mv ^2}{ r }=\frac{3 q ^2}{4 \pi \varepsilon_0 r ^2}$
$ \Rightarrow mvr =\frac{3 q ^2}{4 \pi \varepsilon_0 v }....$(i)
and $\frac{ nh }{2 \pi}= mvr....$(ii)
Using (i) and (ii) and putting $n =1$
$\frac{ h }{2 \pi}=\frac{3 q ^2}{4 \pi \varepsilon_0 v } $
$\Rightarrow v =\frac{3 q ^2}{2 \varepsilon_0 h }$