Question

In a hydrogen atom electron moves in an orbit of radius $5\times {10}^{-11}$m with a speed of $22\times {10}^4$m/s. Calculate current.

Answer 1

Given,

$v=22\times {10}^{4}m/s$

$q=e=1.6\times {10}^{-19}C$

$r=5\times {10}^{-11}m$

Current, $I=\frac{q}{T}$. . . . (1)

Angular frequency, $\omega =\frac{2\pi }{T}$

$\omega =\frac{v}{r}=\frac{2\pi }{T}$

$T=\frac{2\pi r}{v}$. . . .(2)

put equation (2) in (1) , we get

$I=\frac{qv}{2\pi r}$

$I=\frac{1.6\times {10}^{-19}\times 22\times {10}^4}{2\times 3.14\times 5\times {10}^{-11}}=1.121\times {10}^{-4}A$

$I=0.1121mA$