Magnetic Moment

The magnetic dipole moment due to the revolving electron is given by: Where:
- is the current associated with the moving electron,
- is the area enclosed by the orbit of the electron.
Step 1: Current due to the electron The electron is moving in a circular orbit, so the current is defined as the charge passing through a point per unit time. The time period of the electron's revolution is the time it takes to complete one full revolution around the nucleus. The frequency of the electron is: where:
- is the velocity of the electron,
- is the radius of the orbit. The current is given by:
Step 2: Area enclosed by the orbit The area enclosed by the electron's orbit is the area of a circle:
Step 3: Magnetic dipole moment Now, the magnetic dipole moment is: Thus, the expression for the magnetic dipole moment of the atom is: (b) If is the angular momentum of the electron, show that .} Solution: The angular momentum of the electron is given by: Now, substitute from this equation into the expression for the magnetic dipole moment: Thus, we have shown that: