Dhristi JEE 2022-24

Explanation and Formula of Zeeman Effect

The Zeeman effect is an effect in which the light of a spectral line is divided into two or more recurrences when it is under a magnetic field’s ubiquity. This property is named after Pieter Zeeman, a 20th-century physicist from the Netherlands who won the Nobel Prize in Physics and Hendrik Lorentz in 1902 to discover the effect. Understanding the Zeeman effect has led to advancements in electron paramagnetic resonance studies and magnetic field measurements in space, such as those of the Sun and other stars.


The development of quantum mechanics further modified the understanding of the Zeeman effect by resolving which spectral lines were released as electrons were passed from one energy shell to another in their orbit of atomic nuclei. The application of the Zeeman effect can be further extended to understand the molecular lines; sunspots related to Stokes profiles and infrared related spectropolarimetric observations.


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Zeeman Splitting

The pattern and amount of splitting signify that a magnetic field is present and of its strength. The Zeeman splitting is associated with the atomic level’s orbital angular momentum quantum number L. The quantum number L can assume values that are non-negative integers. The formula 2* L+1 can ascertain the magnetic field splitting in terms of levels. The given figure illustrates the Zeeman effect.


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In atomic physics, different letters are used to represent the quantum levels, for L=0, “s” is used; for L=1, “p” is used; for L=2, “d” is used. These denotations are carried on for higher levels as well. It is also customary to precede this designation with the integer principal quantum number n. Thus, the designation "2p" indicates a level that has L equal to 1 and n equal to 2. In order to observe the Zeeman splitting, the Zeeman effect experiment needs to be carried out. This splitting of spectral lines under the magnetic field is also known as Zeeman shifts. 


Polarisation of Spectral Lines

Polarisation effects can be associated with the lines related to Zeeman splitting. Polarisation in this context refers to the direction of the vibration of electromagnetic field lines. For example, polarising sunglasses usually suppress ambient glare because light reflected from surfaces has a specific polarisation. Polarising sunglasses are designed not to pass the polarization of light. 


Zeeman Effect and Stark Effect

Zeeman effect marks the piercing of spectral representations in the occurrence of a solid static external magnetic field. It was named after Pieter Zeeman. The impact of the magnetic field on atoms is defined under this concept. It is similar to this effect, as the spectral outlines are separated into various constituents in the occurrence of a current field.


Stark effect is witnessed when the piercing of spectral outlines is observed beneath the impression of the field of current. These spectral lines are the resultant of radiating ions, atoms, or molecules. When the spectrum of different frequencies of electromagnetic radiation is emitted or absorbed as the transition of electrons between an atom’s various energy levels, a spectrum occurs. 


The signifying difference between Zeeman and Stark effect is that in the Zeeman effect we observe the spectral lines splitting under the influence of a strong externally applied magnetic field, on the other hand, the Stark effect is the phenomenon where spectral lines split under the influence of a strong electric field. The Zeeman effect is analogous to the Stark effect, whereas, the Stark effect is perceived as the electric field that is analogous to the Zeeman effect. Therefore the Stark and Zeeman effect are effects that encompass both the impact of magnetic and electric fields on spectral lines. 


Zeeman Energy

Zeeman energy is the potential energy of a body in a magnetic field external to the same body that is magnetized. It can be represented as:


\[E_{Zeeman} = -\mu \int _{\nu } M.H_{ext} dV\]


Where \[H_{ext}\] is the external field. 


M = local magnetization, and over the volume of the body, the integral is done, This is the statistical average of an analogous microscopic Hamiltonian (energy) for each magnetic moment m, which is, however experiencing a local induction B: 


H = - m . B


Use of Zeeman Effect

  • The Zeeman effect has helped physicists determine the energy levels in atoms and identify them in terms of angular momenta. 

  • Zeeman effect is also applicable to know the magnetic field of space particles and various stars.

  • It is also useful in laboratories to know more about plasma.


Conclusion

This is all about the Zeeman effect and the explanation of the related terms. Understand the concept well with a proper explanation of the terms used.

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FAQs (Frequently Asked Questions)

1. How many kinds of Zeeman effects are there and what are they? What is meant by the Normal Zeeman effect?

There are two types of Zeeman effects

  • Normal Zeeman effect

  • Anomalous German effect

Normal Zeeman Effect: Normal Zeeman Effect is the splitting of spectral lines of an atomic spectrum due to the interaction between the external magnetic field and the orbital magnetic moment.

2. Explain electronic spin movement between two types of Zeeman effect.

Electron Spin

  • Normal Zeeman Effect: Normal Zeeman effect is observed at zero electron spin states.

  • Anomalous Zeeman Effect: This can only be observed in the presence of an electron spin.

3. What is the Magnetic Moment in the Zeeman effect?

  • Normal Zeeman Effect: Normal Zeeman effect occurs due to the presence of the orbital magnetic moment.

  • Anomalous Zeeman Effect: The Anomalous Zeeman effect occurs due to the presence of both orbits having inherent magnetic moments.

4. How does the Zeeman effect help us to know the magnetic field of the sun?

The Zeeman Effect helps to measure the magnetic field of the sun. We can observe the magnetic field of the sun in a plasma state. We can also observe the magnetic spectrum created by the sun in various photos taken by space research organizations which denote how the sun emits the energy and how the magnetic field is created.

5. Define the Normal Zeeman Effect.

The Normal Zeeman effect is one of three types of Zeeman effect. The splitting of an atomic spectrum’s spectral lines due to the interaction within the momentum of the orbital magnetic and the external magnetic field is known as the Normal Zeeman Effect. This effect can be seen in the absence of electron spins. 


When energy is passed on to an atom, the atom gains an excited state. The electrons of that atom can consume energy and move to a higher energy level. Similarly, all electrons of that atom can absorb energy and move to higher energy levels. This provides the absorption spectrum of that atom. It can also be observed as a triplet in the observed spectrum rather than a single spectral line in the expected scope.

6. Define the Paschen Back Effect.

In the presence of a significant external magnetic field, the energy levels of atoms are split up. This splitting is defined well by the Zeeman effect if the splitting is minute compared to the energy variation between the unperturbed groups, i.e., for adequately weak magnetic fields. If the magnetic field is wide enough, it interrupts the coupling within the orbital and spins angular momentum, resulting in a different Zeeman splitting pattern. This effect is termed the Paschen-Back effect. The Paschen-Back effect does have astronomical significance as they are met in some lithium spectra that are observed on the Sun.

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