In a hydrogen atom, the electron revolves round the nucleus `6.8 xx 10^(15)` times per second in an orbit of radius `0.53Å`. What is equivalent magnetic moment ? (Given that `e=1.6 xx 10^(-19)C`).

Explanation

The electron revolving in an orbit is equivalent to a current loop. The magnitude to current is given by ,
`I =(e)/(T) = e xx (1)/(T) = ef= (1.6 xx 10^(-19)) (6.8 xx 10^(15))`
`=1.1 xx 10^(-3) A `
Magnetic moment of equivalent current loop is M= nIA .
Here `n=1 ,I = 1.1 xx 10^(-3) A` and
area ,`A = pi ( 0.53 xx 10^(-10))^(2)`
`:. M = (1)(1.1 xx 10^(-3)) [ pi (0.53 xx 10^(-10))^(2)]`
`=9.7 xx 10^(-24) Am^(2)`