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Grade upto college level Magnetism

An electron in the ground state of hydrogen atom is revolving in anticlock – wise direction in a circular orbit of radius R.

Obtain an expression for the orbital magnetic dipole moment of the electron.

The atom is placed in a uniform magnetic induction B such that the plane – normal of the electron –orbit makes an angle of 30° with the magnetic induction. Find the torque experienced by the orbiting electron.

Question image for An electron in the ground state of hydrogen atom i

Amit Saxena

12 Years agoGrade upto college level

1 Answer

Apoorva Arora

12 Years ago

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

$M=\frac{eL}{2m}$

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 $\tau =M\times B=MBsin30^{0}$ .

Thanks and Regards

Apoorva Arora

IIT Roorkee

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