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,

Now,

The quantity eB/4πm is known as Normal Zeeman Sepration.

*Zeeman Shift :*

*” υ – dυ ” , ” υ ” , ” υ + d υ ”*gives a normal triplet.

**L**and magnetic moment

**μl**.

,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.

*l = 1*to

*l = 0*level in the magnetic field. The

*l = 1*level is splitted into

*(*

*2l + 1 )*= 2 × 1 + 1 = 3 levels corresponding to ml = -1, 0, +1, while the level

*l = 0*

=> 2(0) +1 = 1 level, i.e. this level is unstable.

*υ0*is shifted to :

*υ*0 is frequency of unshifted components &

*υ*1 and

*υ*2 are frequency of shifted components.

Thus, measuring change of wavelength λ we can find the value of e/m.