Question

The electron of a hydrogen atom revolves round the proton in a circular$n^{th}$ orbit of radius $r_n=\frac{{\epsilon }_0{n}^2{h}^2}{\pi m{e}^2}$ with a speed $V_n=\frac{e^2}{2{\epsilon }_{0}nh}$. The current due to the circulating charge is proportional to:-

• A. $e^2$
• B. $e^5$
• C. $e^3$
• D. $e^6$

Answer 1

The correct option is B $e^5$

From given values of $r_n$ and $V_n$,

the time period of revolution can be found as $T=\frac{r_n}{V_n}$

and the current is $I=\frac{q}{T}=\frac{e}{T}=\frac{e{V}_n}{r_n}$

putting all values $I=\frac{\pi m{e}^5}{2{ϵ}_0^2{n}^3{h}^3}$ so $I\propto e^5$