The normal Zeeman effect can be explained by Classical electron theory as well as Quantum theory without taking electron spin. Now, let us explain Normal Zeeman effect with the help of mathematical expression.
Normal Zeeman Effect
When an external magnetic field B is applied perpendicular to the direction of motion of the electron, it will experience a Lorentz force i.e.
Now, we have:
Also, we have,
The quantity eB/4πm is known as Normal Zeeman Separation.
Zeeman Shift :
The μl and L are oppositely directed when the atom is placed in magnetic field B which is acting along the z-axis when L processes around the magnetic field ( Larmor Precession) with quantized components.
By Larmor’s theorem, the angular velocity of Precession is given by :
The interaction energy of such precession is equal to the product of angular velocity and projection of L along that field, i.e.
Now, ml takes (2l + 1 ) discrete values. It is each energy level for a given value of l, is shifted into ( 2l + 1) energy levels called Zeeman level.
=> 2(0) +1 = 1 level, i.e. this level is unstable.
The change in frequency in normal Zeeman effect is given by :
Thus, measuring the change of wavelength λ we can find the value of e/m.
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