# ZEEMAN EFFECT

Zeeman in 1896, observed that the spectral lines are split up into components when the source emitting those spectral lines is placed in a strong magnetic field. He further observed that these components are polarized. The two types of Zeeman effect has been observed which are known as Normal Zeeman effect and Anomalous Zeeman effect. The schematic diagram of experimental arrangement for observing Normal Zeeman effect is shown in Figure 10.3.

FIGURE10.3 Schematic diagram of Zeeman effect

The interaction of the magnetic field B with the magnetic moment of the electron system results in splitting of the energy levels: and hence in spectral lines. The magnetic moment the electron may arise from its orbital as well as its spin motion. We know that the torque experienced by a magnet in a magnetic field is µ × B, where µ is the magnetic moment potential energy of the magnetic dipole (the rotating electron around nucleus behaves like tiny magnetic dipole) is given by – µB.

As such, if B is not too strong, the potential energy of orientation of an atom in a magnetic field B is given by (- µA.B), where µA is the magnetic moment of atom. Let the energy atomic level is E0, in absence of B, then the energy of the system in presence of magnetic field will be given by

E = E0 – [µA.B] = E0 – µz B                                               … (1)

where, µz is the Z component of µA and B is parallel to the Z direction.

Normal Zeeman Effect

The Normal Zeeman pattern observed due to transition between singlet (s = 0) states. The effect can be explained by classical theory as well as from the quantum theory of electron  without considering the electron spin.

The current constituted by an electron of mass m and charge – e in an atom will be given as

Let the loop area of electron motion is A, then from electromagnetic theory, the magnitude of orbital magnetic moment

The quantity µB=eh/2m is called as ‘Bohr magneton’ which has the numerical value 9.27 × 10-24 A-m2. The µB forms a natural unit for the measurement of atomic magnetic moments. Moreover the introduction of a magnetic field superimposes a precessional motion on the orbital motion of the entire orbit of the electron, about
the direction of the magnetic field, with angular velocity ω = eB/2m. The angular frequency is known as the Larmor precessional frequency and the above statement is referred as ‘Larmor theorem’.

Quantum Mechanical Explanation of Zeeman Effect: In magnetic field the electron of
atom with magnetic moment µl acquires additional energy due to its precessional motion which is given as

Here EB corresponds to the energy of spectral line in presence of B and E0 is the energy of the system without B.

In terms of frequency

Expression for Zeeman shift: The precessional frequency of electron in magnetic field is

Anomalous Zeeman Effect

The anomalous Zeeman effect is observed due to transition between multiplet states. In this effect, the spectral lines are observed in more than three components after splitting. The anomalous Zeeman effect can be explained by considering the spin motion of electron.

Let B is small enough for Zeeman splitting, and hence the magnetic energy can b
considered as a very small perturbation. Now due to the torque on magnetic moment, J will precess around B at a smaller rate compared to precession rate of orbital and spin angular momentum about J. Since Land S precess about J, µL and µS must precess about J.

According to the quantum theory, the spin and orbital magnetic moments are given as

It is clear that each unit of spin angular momentum contributes twice is the unit of hence the magnetic moment of atom  is not antiparallel to J. The Figure 10.5 depicts the various momenta and their corresponding magnetic moments.

This is additional energy due to presence of the magnetic field.

Examples of Normal and Anamalous Zeeman pattern.

1. Zeeman effect in 1F31D2 transition: For states 1F3 and 1D2, the values will be 3 and 2. Hence under influence of B these states will spill in (2L + 1) substates i.e.,  for 1F3 there will be 2 × 3 + 1 = 7 and for 1D2there will be 2 × 2 + 1 = 5 substatesMultiplicity 25 +1 = 1 for 1F3 S = 0, J = Land 2S + 1 = 1 for 1D2S = 0 J=L.Therefore the value of Lande ‘g’ factorwill be 1 in both the cases.

2.    Zeeman Effect in D1 and D2 lines of sodium: The D1 and D2 lines in sodium are observed due to the transition between 2P1/22S1/2 states. It is a doublet-doublet transition and hence anomalous Zeeman pattern will be observed. The term values, ‘g’ factor and energy shift of spliting levels i.e., gml are given in Table 1.

Hence we observe four component lines in D1 line and six components for D2 line of
sodium under influence of weak magnetic field.