# Zeeman Effect

## Zeeman Effect:

A spectral line emitted by the excited atoms is split up into a doublet or a triplet when the emitting atoms are placed in a magnetic field. This effect of the splitting of a spectral line under the action of a magnetic field is known as the Normal Zeeman Effect.

To produce the Zeeman Effect, the source of light such as a sodium lamp or a mercury arc or gas discharge in a Geissler tube is placed between the poles of a powerful electro-magnet as shown in the above figure. The light coming from the source is examined by means of a spectroscope of high resolving power. In order to view the light parallel to the magnetic field, a hole is drilled in one of the pole pieces along the axis of the magnet.

When no magnetic field is applied, the spectroscope is focused on one of the lines in the spectrum of the source of light. When a magnetic field is applied, it is observed:

(1) That when the light is viewed in a direction perpendicular to the magnetic field, three component lines are observed. One of the lines is in the same position as the original line and the other two lines are on the two sides of the original line. The outer two lines, when observed by means of a Nicol prism as an analyzer, are polarized at right angles to the undisplaced line. This effect is known as the Transverse Zeeman Effect.

(2) When the light is viewed in a direction parallel to the direction of the field, there is no line in the position of the original line, only two outer lines are present. These lines are found to be circularly polarized in opposite directions. This effect is known as the Longitudinal Zeeman Effect.

The Normal Zeeman effect is explained by Lorentz’s electron theory. Consider an electron moving in a circular orbit of radius r with a velocity ν as shown in the below figure. The centripetal force is, F = (mν2)/r. If an external magnetic field is applied, an additional force acts which is directed perpendicular to the direction of motion of the electron. This force is also perpendicular to the direction of the magnetic field and is along the radius. When/this force acts inwards along the radius, the velocity of the electron increases. When this force acts outwards along the radius, the velocity of the electron decreases. Suppose, this force due to the magnetic field = F1 and let the velocity of the electron be increased to ν1 by the application of the magnetic field. Then, F1 = Beν1. Suppose, this force is directed towards the centre, total force along the radius = F + F1 = (mν2)/r + Beν1.

When the electron moves in the opposite direction, the magnetic field produces a force in the opposite direction and the velocity decreases to ν2. In that case

## Alternative Treatment:

Consider an electron moving in a circular orbit of radius r with velocity ν.