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An electron in an atom is revolving roun...

An electron in an atom is revolving round the nucleus in a circular orbit of radius `5.3 xx 10^(-11) ` m, with a speed of `2 xx 10^(6) ms^(-1)`. The resultant orbital magnetic moment and angular momentum of the electron is ......
Take charge of electron `= 1.6 xx 10^(-19) C`,
mass of electron `= 9.1 xx 10^(-31)` kg.

Text Solution

Verified by Experts

The current flowing in circular path of electron with frequency f is `I= fe`
But `f= (omega)/( 2pi ) " " therefore I= (omega e)/( 2pi) `
but `omega = (v)/( r)`
`therefore I= (ve)/( 2pi r)`
`m= IA`
`= (ve)/(2pi r) xx pi r^(2) `
`= (1)/(2) ver`
`= (1)/(2) xx 2 10^(6) xx 1.6 xx 10^(-19 ) xx 5.3 xx 10^(-11)`
`= 8.48 xx 10^(-24) "Am"^(2)`
Angular momentum `L=pr`
`-m_(e) vr " "("where" p = mv)`
`L= 9.1 xx 10^(-31) xx 2 xx 10^(6) xx 5.3 xx 10^(-11)`
`= 96.46 xx 10^(-36) `
`therefore L= 9.65 xx 10^(-35)` Nms
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