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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
one month ago

Answers : (1)

Arun
15841 Points
							
 
  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}.
one month ago
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