Q. The electron of hydrogen atom is considered to be revolving round in circular orbit of radius $h^{2}/me^{2}$with velocity $\frac{e^{2}}{h},\ $where $h = h/2\pi$. The current $i$ is
A) $\frac{4\pi^{2}me^{5}}{h^{2}}$
B) $\frac{4\pi^{2}me^{2}}{h^{3}}$
C) $\frac{4\pi^{2}m^{2}e^{5}}{h^{3}}$
D) $\frac{4\pi^{2}me^{5}}{h^{3}}$
Explanation
(d) $i = \frac{e}{t} = \frac{e}{2\pi r/v} = \frac{ev}{2\pi r}$
Here, $v = \frac{e^{2}}{h}and\ r = h^{2}/me^{2}$
$\therefore i = \frac{e(\frac{e^{2}}{h})}{2\pi(h^{2}/me^{2})} = \frac{e^{3} \times me^{2}}{2\pi h^{3}} = \frac{me^{5}}{2\pi h^{3}}$
$i = \frac{4\pi^{2}me^{5}}{h^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.