Question

From Exercise 11 data. Obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron ? Explain.

Answer 1

Given
`B=6.5 G=6.5 xx10^(-4)T, V=4.8xx10^(6) m//s, e=1.6xx10^(-19)C`
`m_(e)=9.1xx10^(-3) kg`
`(nV^(2))/(r )= q V B rArr (mV)/(r )=q B`
If angular velocity of electron is `omega`, then
`V=r omega`
`(m r(omega))/(r )=qB`
`omega =(qB)/(m)`
`2pi n=(qB)/(m) rArr n=(qB)/(2 pi m)`
Frequency of revolution of electron in orbit
`v=(Bq)/(2pi m)=(Be)/(2pi m_(e))=(6.5xx10^(-4)xx1.6xx10^(-19))/(2xx3.14xx9.1xx10^(-31))=18.18xx 10^(6) Hz.`