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An electron in a circular orbit of radiu...

An electron in a circular orbit of radius 0.05 mm performs `10^(16)` revolutions per second. The magnetic moment due to this rotation of electron is `("in Am"^(2))`

A

`2.16 xx 10^(-23)`

B

`3.21 xx 10^(-22)`

C

`3.21 xx 10^(24)`

D

`1.26 xx 10^(-23)`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, radius of the orbit, r = 0.05nm
`= 0.05 xx 10^(-9)m`
Frequency, `v = 10^(16)rev//s`
The electron moving in a orbit behaves as a current loop.
The current due to orbit motion of electron is
`I = ev`
Area of the loop, `A = pir^(2)`
`therefore` Magnetic moment of the loop, `M = IA = evpur^(2)`
`therefore M = 1.6 xx 10^(-19) xx 10^(16) xx 3.14 xx (0.05 xx 10^(-9))^(2)`
`= 0.0126 xx 10^(-21) Am^(2) = 1.26 xx 10^(-23)A m^(2)`
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