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

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Solution

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mvR=h2π or v=h2πmR

Now time period, T=2πRv=2πRh/2πmR=4π2mR2h

Magnetic moment, M=iA

Where, I=chargetime period=e4π2mR2h=eh4π2mR2

and A=πR2

∴M=(πR2)(eh4π2mR2) or M=eh4πm

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

Where, I=chargetime period=e4π2mR2h=eh4π2mR2

and A=πR2

∴M=(πR2)(eh4π2mR2) or M=eh4πm

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

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