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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

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

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1 Answers

Arun
25763 Points
2 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}.

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