Short Answer

The magnetic moment of an electron is a measure of how strongly the electron behaves like a tiny magnet. This property comes mainly from the electron’s spin and partly from its orbital motion around the nucleus. Because of its magnetic moment, an electron can interact with magnetic fields.

The magnetic moment determines how electrons align in a magnetic field, which affects atomic structure, magnetism in materials, and many physical phenomena. It is expressed in a unit called the Bohr magneton, which is the standard unit for measuring electron magnetic strength.

Detailed Explanation :

Magnetic moment of an electron

The magnetic moment of an electron is a fundamental property that makes the electron behave like a small bar magnet. This magnetic moment arises due to two main reasons: the spin of the electron and the orbital motion of the electron around the nucleus. In classical physics, a moving charge produces a magnetic field. In quantum physics, even though the electron is not physically spinning like a ball, its intrinsic spin creates a magnetic effect.

The magnetic moment tells us how strongly an electron will interact with a magnetic field. This interaction plays an essential role in atomic structure, chemical bonding, spectroscopy, magnetic materials, and many modern technologies. The most widely used measure of magnetic moment is the Bohr magneton, represented by μᴮ, which acts as the natural unit for the magnetic moment of electrons.

Spin magnetic moment

One important contribution to the electron’s magnetic moment comes from its spin. The electron has a spin value of 1/2, and this gives rise to a spin magnetic moment. When an electron is placed in a magnetic field, its spin can align either parallel or antiparallel to the field. These two orientations correspond to two different energy levels, which is the basis for phenomena like:

Electron Spin Resonance (ESR)
Magnetic Resonance Imaging (MRI)
Zeeman effect

The formula for the spin magnetic moment is:

μₛ = gₛ × μᴮ × s

Here,

gₛ is the spin g-factor (approximately 2.0023),
μᴮ is the Bohr magneton,
s is the spin quantum number of the electron (1/2).

This means the spin magnetic moment is slightly more than one Bohr magneton.

Orbital magnetic moment

In addition to spin, an electron moving in an orbit around the nucleus creates a circular electric current, which produces a magnetic moment. This is called the orbital magnetic moment. In classical terms, it is similar to a charged particle moving in a loop.

Quantum mechanically, the orbital magnetic moment is determined by the orbital angular momentum quantum number l. Higher orbital angular momentum means a stronger magnetic moment.

The orbital magnetic moment is given by:

μₗ = μᴮ × √[l(l + 1)]

This shows that electrons in s-orbitals (l = 0) have no orbital magnetic moment, while p, d, and f orbitals contribute significantly.

Total magnetic moment

The total magnetic moment of an electron inside an atom is a combination of both orbital and spin magnetic moments. These two moments interact through a process called spin-orbit coupling, which causes splitting of energy levels. This splitting helps explain fine structure in atomic spectra.

The total magnetic moment plays a central role in:

Spectral line structure
Magnetic behavior of atoms
Magnetic properties of solids

Bohr magneton

The Bohr magneton is the standard unit of the magnetic moment of an electron:

μᴮ = (eħ) / (2mₑ)

Where

e is the charge of the electron,
ħ is reduced Planck’s constant,
mₑ is the mass of the electron.

Its approximate value is:

μᴮ ≈ 9.27 × 10⁻²⁴ J/T (joule per tesla)

This small value shows how tiny the magnetic moment of a single electron is, but when many electrons align together, they create strong magnetic effects, such as in magnets.

Role of magnetic moment in atoms

The magnetic moment affects the arrangement of electrons in atoms and explains why some atoms or materials are magnetic. When electrons in an atom have unpaired spins, each contributes its magnetic moment, and the atom becomes magnetic.

The magnetic moment explains:

Paramagnetism (attraction to magnetic field)
Diamagnetism (weak repulsion)
Ferromagnetism (strong permanent magnetism)

Metals like iron, cobalt, and nickel show ferromagnetic behavior because of aligned electron spins.

Significance in modern physics and technology

The magnetic moment of electrons is extremely important in many technologies:

Magnetic Resonance Imaging (MRI)

MRI uses the alignment of nuclear spin magnetic moments in a magnetic field to produce detailed images of the human body.

Spintronics

A modern field where devices use electron spin instead of charge to store and transfer data. Hard drives and advanced memory devices use this concept.

Quantum computing

Some qubits are built using electron spins, where spin-up and spin-down represent different quantum states.

Spectroscopy

Electron magnetic moments help explain fine structure and splitting in atomic spectra.

Magnetism in materials

Understanding the electron’s magnetic moment helps explain how magnets work.

Experimental evidence

The magnetic moment of the electron was first detected through the Stern–Gerlach experiment, which showed that atoms are deflected into discrete paths when passed through a magnetic field. Later, precise measurements confirmed the value predicted by quantum theory.

Today, the magnetic moment of the electron is measured with extraordinary precision and remains one of the most accurately known physical quantities.

Conclusion

The magnetic moment of an electron is a fundamental property that makes it act like a tiny magnet. It arises from both the spin and orbital motion of the electron. Expressed in units of the Bohr magneton, it plays a crucial role in explaining atomic structure, magnetic materials, spectroscopy, and modern technologies such as MRI and spintronics. Understanding magnetic moment helps us understand the microscopic behaviour of matter and many practical applications in physics and engineering.