Question

If the expression for the orbital magnetic moment of the electron is $M=Xπmeh $. Find X?

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Updated on : 2022-09-05

Solution

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Correct option is A)

$mvR=2πh $ or $v=2πmRh $

Now time period, $T=v2πR =h/2πmR2πR =h4π_{2}mR_{2} $

Magnetic moment, $M=iA$

Where, $I=time periodcharge =h4π_{2}mR_{2} e =4π_{2}mR_{2}eh $

and $A=πR_{2}$

$∴M=(πR_{2})(4π_{2}mR_{2}eh )$ or $M=4πmeh $

Direction of magnetic moment $M$ is perpendicular to the plane of orbit.

Where, $I=time periodcharge =h4π_{2}mR_{2} e =4π_{2}mR_{2}eh $

and $A=πR_{2}$

$∴M=(πR_{2})(4π_{2}mR_{2}eh )$ or $M=4πmeh $

Direction of magnetic moment $M$ is perpendicular to the plane of orbit.

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