Zeeman Effect
The 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 Geissler tube is placed between the poles of a powerful electromagnet. 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 of the pole pieces along the axis of the magnet.
When an magnetic light is applied the spectroscope is focused on one of the 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 ads an analyzer, are polarized at right angles to the undisplaced lines. This effect is known as transverse Zeeman effect.
When the light is viewed in a direction parallel to the direction of the magnetic field, there is no line in the position of the original lien and only tow outer lines are present. The lines are found to be circularly polarized in opposite directions. This effect is known as longitudinal Zeeman effect.
The normal Zeeman effect is explained on Lorentz electron theory. Consider an electron moving in a circular orbit of radius r with a velocity v. The centripetal magnetic field is applied, an additional force acts which is directed perpendicular of the direction of motion of the electron. The force is also perpendicular to the direction of the magnetic field along the radius. When this force acts inwards 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 r1 by the application of the magnetic field. Then F = Hev1.
Suppose this force is directed towards the centre, then the total force along the radius
But, v = r ω, and v1 = r ω1
When ω and ω1 are the respective angular velocities.
From equation (i)
m r ω12 – m r ω2 = H e r ω1
(ω1 + ω) is approximately equal to 2 ω1
If v1 and v are the frequencies then, ω1 = 2π v1, and 2πv
When the electron moves in the opposite direction, the magnetic field produces a force in the opposite direction and the velocity decreases to v1. In that case,
But, v2 = rω2 and v = rω
m r ω22 – m r ω2 = – H e r ω2
From (iii) and (iv), we get
Δ v in each case = (e H)/(4πm) (v)
This shows that the two lines are displaced equally on the two sides of the original line.
The quantity (e H)/(4πm) is known as normal Zeeman separation. Knowing the values of Δ v and H, e/m can be calculated. The value of e/m calculated from the measurements of Zeeman effect = 1.757 × 1011 C/kg and it is in agreement with the value of e/m of the electron obtained from Thomson’s experiment.
This experiment established that the electron in the atom is responsible for the emission of spectral lines.
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