# Introduction

In this particular article Explanation of normal Zeeman effect, we are going to discuss basic information related to Explanation of normal Zeeman effect along with its vector model.

## Explanation of normal Zeeman effect(Zeeman effect without electron spin)

If a source of light producing a spectral line is placed in a magnetic field and the light examined with a spectroscope, one observes that the spectral line splits into a number of components. Consequently produced this effect is called the Zeeman effect. And it arises from the interaction between the applied magnetic field and the total magnetic moment due to orbital and spin angular momenta of the atom.

When the spectral line splits into three polarized components, the effect is called the normal Zeeman effect. And it occurs only when spin magnetism does not contribute, that is, it is Zeeman effect without electron spin. Hence in the case of normal Zeeman effect, and the emitted or absorbed line of an atom splits into three components under the influence of a magnetic field. The energy and wavelength of the central component (π) are unchanged with respect to the original values. And the π-component is also linearly polarized parallel to the magnetic field.

### (Additional information)

The two other component (σ) are shifted by equal wavelength intervals higher and lower than the original wavelength. Hence the sigma components are polarized perpendicular to the magnetic field. The extent of the shift depends on the applied magnetic field strength. The sum of the intensity of the three components is always equivalent to the intensity of the original line. The distribution of the energy or intensity between components is σ:π:σ=25:50:25

An observer looking along a line perpendicular to the magnetic field sees a central component polarized parallel to the field and on either side a component polarized perpendicular to the field; While if he looks along the magnetic field through a hole bored in one of the polepieces, and the central line disappears and the two lateral components are circularly polarized; further the latter rotate in opposite directions.

#### Note

(The normal Zeeman effect occurs in only those spectral lines which arise from transitions between singlet terms (total spin S=0 terms). Thus, in these states, at least two electrons (↑↓) contributes in such a way that their spins are coupled to zero. Singlet lines are the main resonance lines of the alkaline earth metals(Be, Mg, Ca(422.7nm), Ba(553.5nm) and the Zinc group metals(Zn, Cd, Hg).)

##### Explanation of normal Zeeman effect(Vector Model)

Let’s understand Normal Zeeman effect by taking an example. Let us consider an atom with one-electron outside the closed shells and completely ignore the electron spin and its interaction with the applied external field. And let the original angular momentum od atom is L. Then, the orbital magnetic moment of the atom is given by

μL=-(e/2m)L=-μB(L/ ~~h~~)…….(1)

where μB=e~~h~~/2m is a constant known as Bohr magnetron. The vector μL is directed opposite to the vector L. Hence Let the atom is placed in a magnetic field B pointing in the z-direction, i.e B=(0,0, B). The additional energy of the atom due to the interaction of magnetic moment with the magnetic field is

Eint=-μL.B = (μB/ ~~h~~)(L.B)

= (μB.B/ ~~h~~)Lz

###### explanation

In the presence of the magnetic field B, the angular momentum vector L and the magnetic moment μL, which is coupled to L, process together around the field axis B. Hence the vector model uses pictures like this. And the cone for the angular momentum is drawn with side √l(l+1) ~~h~~ and represent the magnitude of the angular momentum. The vector representing the state of angular momentum.

The vector representing the state of angular momentum can be thought of as lying with its tip on any point of the mouth of the cone. Since we have chosen the direction of the magnetic field as the z-axis,i.e., B=(0,0, B), due to precession motion, and the Lx and Ly projections on the magnetic axis are indefinite and average out of zero. Hence Only the projection along the magnetic field direction. And that is Lz has a definite value m1~~h~~ where m1 can have any one of the following 2l+1 possible values:

ml=l,l,-1,…,-l…..(3)

as a result of additional energy, Eq.(2), of the atom in the magnetic field becomes (using Lz=ml~~h~~)

Eint=(μBB/ ~~h~~)Lz = mlμBB…..(4)

It has 2l+1 possible values. And thus an energy level specified by orbital angular quantum number l splits into 2l+1 levels. according to (4) the splitting is proportional to ml and B. The origin of this splitting is that magnetic field breaks the spherical symmetry characteristic for the unperturbed atom. With the selection rules for optical transitions.

Δml=0 or ±1….(5)

The above derivation leads to the splitting of spectral lines in three lines, an effect known as the normal Zeeman effect.