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Question

An electron in the ground state of hydrogen atom in revolving in anticlockwise direction in a circular orbit of radius R (see fig)If the expression for the orbital magnetic moment of the electron is M=ehXπm. Find X?

Solution
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In ground state (n=1) according to Bohr's theory:mvR=h2π or v=h2πmRNow time period, T=2πRv=2πRh/2πmR=4π2mR2hMagnetic moment, M=iAWhere, I=chargetime period=e4π2mR2h=eh4π2mR2and A=πR2∴M=(πR2)(eh4π2mR2) or M=eh4πmDirection of magnetic moment →M is perpendicular to the plane of orbit.

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