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# an electron in the ground state of the hydrogen atom is revolving in the anti-clockwise direction in a circular orbit. the atom is placed normal to the electron orbit and makes 30 degrees with the magnetic field. find the torque experienced by the electron

Arun
25763 Points
3 years ago

1. The electron performs uniform circular motion with period of revolution T. If R is the radius of the orbit, v is the orbital velocity, then,
$T=\frac{2\pi R}{v}$
current =$I=\frac{e}{T}=\frac{ev}{2\pi R}$
magnetic moment is given by M= current X Area
$M=IA=\frac{ev}{2\pi R}\times \pi R^{2}=evR/2$
multiplying and dividing by mass
$M=\frac{eL}{2m}$
1. The revolving electron forms a dipole with a dipole moment derived above, so, the torque acting on a dipole due to a magnetic field is given by$\tau =M\times B=MBsin30^{0}$.