The explanation of anomalous Zeeman effect is explained by taking the spin the electron.

## Anomalous Zeeman Effect

In the vector model of the atom, the angular momentum **L **and spin angular momentum vector precess around the total angular momentum **J**.

When the atom is placed in weak magnetic field

**B**along**z**, the magnetic moment of atom associated with**j**( μj**)**and**j**precess slowly around the magnetic field following quantum condition, i.e.where mj takes ( 2j + 1) values from -j to +j. Thus due to the precession of

Let us consider a system of the single valence electron, we have :

**J**around**B****,**the energy level is splitted into 2J + 1 levels called Zeeman levels.Let us consider a system of the single valence electron, we have :

then, the magnetic field of an atom is given by :

Using Cosine law :

The importance of g factor is that it gives directly the relative separations of Zeeman levels.

The expression for g-factor for multi electron under L – S coupling is same as above. The expression for total magnetic moment of atom now becomes :

Let us now, calculate magnetic interaction energy. From the last expression we’ve :

Thus, g determines the ratio of the total magnetic moment to the total angular momentum in states where the angular momentum is partly orbital and partly spin. (For S = 0 and so on

J=L,g=1;for L = 0 and so J = S , g = 2).

By Larmor’s theorem, the angular velocity of the precession of

**J**around the field**B**is :Thus, Anamolous Zeeman effect is explained with the help of the above expression.

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