ZEEMAN EFFECT

The Zeeman Effect

1. Historical Background

• When there is a strong magnetic field around, spectral lines split apart. This is called the Zeeman effect.
• Background: Pieter Zeeman found this effect in 1896 and won the Nobel Prize in Physics for it in 1902.
• It helped us learn more about spectroscopy and showed how magnetic fields can change the way atoms behave.

2. The Basic Idea

• When there isn't a magnetic field around, atoms give off light at certain wavelengths that show changes in energy levels.
• When a magnetic field is applied, these energy levels move because the magnetic field interacts with the electrons' magnetic moments.

3. An Explanation of the Result

• Energy Level Splitting: Atoms' energy levels split into several smaller levels, called Zeeman sub-levels. This makes a spectrum with many lines that are very close to each other.

The Normal and Anomalous Zeeman Effect:

• The normal Zeeman effect is seen in light as a single spectral line that splits into three parts (the π and σ lines) when a weak magnetic field is introduced.
• Anomalous Zeeman Effect: This happens when fine structure is present; it can lead to more than three components and is caused by extra problems in the structure of the energy levels.

4. Treatment with Quantum Mechanics

• The Hamiltonian operator lets us describe how the magnetic moments and the magnetic field interact using quantum mechanics.
• The energy of a magnetic moment in a magnetic field (B) is given by E_B = -vecμ ⋅ vecB, where (vecμ) is the magnetic moment vector.
• The changes in energy cause different spectral lines to show up, which can be analysed using the rules of quantum physics.

The Paschen-Back Effect

• People have seen the Paschen-Back effect when the magnetic field strength is a lot bigger than when the Zeeman effect is happening.

1. History

• It was named for Friedrich Paschen and Hermann Back, two scientists who did a lot of research on it in the early 1900s.
• In this case, the magnetic field is strong enough to separate the orbital and spin magnetic moments of electrons fully.

2. Primary Features

• The Zeeman effect has pretty simple line splitting, but the Paschen-Back effect has more complicated patterns of line splitting.
• When strong magnetic fields are applied, the spectral lines will change their order, which means that the electrons will be in a different quantum state.

3. Mechanism of the Effect

• A strong magnetic field changes the way that the magnetic moments of electrons interact with each other.
• The electrons are mostly affected by the nucleus's magnetic field, not its electric field. This changes the way their energy is organised.

4. Quantum Mechanical Treatment

• The Hamiltonian for the Paschen-Back effect needs a more complicated way of dealing with the electron states, taking into account both the spin and the angular momentum of the orbital.
• The transitions between the new sub-levels will be shown by the results of quantum physics.

Zeeman and Paschen-Back Effects Side by Side

1. Field Strength

• The Zeeman Effect can be seen when magnetic fields are weak.
• The Paschen-Back Effect needs strong magnetic fields to work.

2. Interaction of Energy Levels

• The Zeeman Effect involves the mixing of orbital and spin states.
• The Paschen-Back Effect is dominated by magnetic field interactions, making states stand out more.

3. Patterns for Splitting Lines

• Zeeman Effect: Simple splitting into more than one line.
• Paschen-Back Effect: Arrangements that are more complicated with more lines.