What is the spin quantum number?

The spin quantum number is the fourth quantum number and indicates the orientation of the intrinsic angular momentum of an elementary particle (such as an electron or a quark), of a composite particle (such as neutrons and protons), or of an entire atomic nucleus . As such, it is a number that represents, along with the other three quantum numbers, a particular quantum state of a subatomic particle.

This quantum number was discovered during the first quarter of the 20th century, after much more precise measurements of atomic emission line spectra were obtained. A closer inspection of these emission lines showed that they were not individual lines but multiples of lines. This could only be explained by attributing to the electrons a fourth quantum number of angular momentum that could be interpreted as the direction of rotation of the electron around its own axis , similar to how a top (spinning top) or the earth revolves around to yours. In fact, this is the reason why it is called spin, since said word comes from the English word spin which means to spin.

Since the electron has an electrical charge, this rotation generates a small magnetic field that is directed along the axis of rotation. The electron can only have two opposite spins (+1/2 and -1/2) so it can generate one of two possible magnetic fields pointing in opposite directions. This magnetic field is responsible for the doubling of the emission lines.

What are the other quantum numbers?

Before the discovery of spin, only 3 quantum numbers were known, which arise from the mathematical solution of the Schrödinger equation. These are:

• Principal quantum number or energy level (n) . This quantum number is associated with how close an electron is to the nucleus. The smaller it is, the closer to the center it will be.
• Secondary quantum number or angular momentum ( l ). This quantum number is associated with the shape of the orbital that an electron occupies.
• Magnetic quantum number (m _l ) . Associated with the orientation in space of atomic orbitals.

Taken together, each combination of these three quantum numbers defines a unique atomic orbital for an electron, while spin identifies a particular electron.

Different values ​​of spin for different types of particles

Spin is an intrinsic property of elementary particles, just as electric charge is. Also, like electric charge, particles can only have certain spin values ​​with opposite signs. In fact, the spin makes it possible to distinguish two different classes of particles in nature, according to the possible spin values ​​they can have, which are fermions and bosons. This classification of particles comes from the current model of matter, called the standard model.

The Fermions

Fermions are the particles that are part of what we know as matter: everything that has mass and occupies a place in space. This family of particles includes quarks and leptons (including electrons), which are characterized by complying with the Pauli exclusion principle, and by having spins of +1/2 or -1/2 ( which is usually represented as ↑ and ↓ or spin up and spin down).

When these elementary particles join together to form composite particles (hadrons), different spin numbers such as 3/2 and -3/2 can be obtained.

The Bosons

The boson family consists of particles that do not follow the Pauli exclusion principle and are characterized by having a spin of 1. It is believed that elementary bosons can exist with other spin values ​​such as 0, 2, 3, etc. It is believed that these particles are responsible for the existence of all known forces (electromagnetic force, gravitational force, strong nuclear force and weak nuclear force).

Properties of the spin quantum number

• It is represented by the symbol m _s or by s.
• Being a quantum number, its value is quantized, which means that it can only acquire certain values ​​that are multiples of a minimum amount (the quantum). As explained a moment ago, the spin can only take values ​​of +1/2 and -1/2 for fermions, and 1 for bosons (although there may be other bosons with different spins).
• The spin can only take on values ​​that are integer multiples of ħ/2, where ħ is the reduced Plank constant (h/2π).
• If you measure the spin of an electron along a magnetic field, you will only get values ​​of ħ/2 or – ħ/2.