Now, let us explain Noraml Zeeman effect with the help of mathematical expression.
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 Sepration.
Zeeman Shift :
,where e and m are charge & mass of electron.
The μl and L are oppositely directed when the atom is placed in magnetic field B which is acting along z-axis, when L precesses around the magnetic field ( Larmor Precession) with quantised components.
By Larmor’s theorem, the angular velocity of Precession is given by :
The interaction energy of such precession is equal to 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.
Thus, measuring change of wavelength λ we can find the value of e/m.