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Question

Find the orbital magnetic dipole moment of the electron in a hydrogen atom.

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Solution

The orbiting behaves as a current loop.The equivalent current
i=net chargetime of revolution=eT=efrot
Now, magnetic dipole moment μ=niA
n= number of the turns of the loop =1,
A= area of the loop =πr2
μ=(1)(efrot)(πr2) μ=πer2frot
Putting the values of frot and r we obtain,
μ=πe(n2h2ε0πme2Z)(mZ2e44ε20h3n3)=ehn4πm

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