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An electron in a hydrogen atom is moving...

An electron in a hydrogen atom is moving with a speed of `2.3 xx 10^(6) ms^(-1)` in an orbit of radius `0.53 Å`. Calculate the magnetic moment of the revoling clectron.

Text Solution

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`v = 2.3 xx 10^(6) ` m/s
` r = 0.53 Å = 0.53 xx 10^(-10) `m
Current , ` I = e/T = e/((2 pi r)/ v) = (ev)/ (2 pi r) `
` I = (1.6 xx 10^(-16) xx 2.3 xx 10^(6))/(2xx 3.14 xx 0.53 xx 10^(-10))`
` I = 1.105 xx 10^(-3) A`
` :. ` Magnetic moment , `M = I A`
`M = I (pi r^(2))`
` = 1.105 xx 10^(-3) xx 3.14 xx (0.53 xx 10^(-10))^(2) `
` = 9.75 xx 10^(-24) Am^(-2)`
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