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 isM=Xπmeh. Find X?
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Updated on : 2022-09-05
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Correct option is A)
In ground state (n=1) according to Bohr's theory: mvR=2πh or v=2πmRh
Now time period, T=v2πR=h/2πmR2πR=h4π2mR2
Magnetic moment, M=iA Where, I=time periodcharge=h4π2mR2e=4π2mR2eh and A=πR2 ∴M=(πR2)(4π2mR2eh) or M=4πmeh Direction of magnetic moment M is perpendicular to the plane of orbit.