## Spin of Subatomic Particles

# Spin of Subatomic Particles

Spin as a classification method

Spin, s, is the rotation of a particle on its axis, as the earth spins on its axis. The spin of a particle is also called intrinsic angular momentum. Angular momentum is momentum (mass times velocity) times the perpendicular lever arm (distance between point of rotation and application of force). An intrinsic property is one that depends on the essential nature of an object. The total angular momentum of a particle is the spin combined with the angular momentum from the moving particle.

## Spin of the electron

The idea of spin has been around for a long time. In 1925 G. E. Uhlenbeck and S. Goudsmit proposed that the electron has a spin, and the spin of the electron has been proven experimentally. The spin of the electron combined with its electric charge gives the electron magnetic qualities because of the electromagnetic force.

## Spin in quantum mechanics

The spin of microscopic particles is so small it is measured in special units called “h-bar,” related to Planck’s constant, h, which is defined as 4.1× 10^{-21}MeV seconds. h-bar is defined to be h divided by two and by pi (3.14159…).

Quantum mechanics is a branch of physics focusing on subatomic particles, and dealing in probabilities. One of the rules of Quantum mechanics says spin can only have certain values. Another way of saying this is spin must be “quantized.” Particles with spin values of one-half h-bar, three-halves h-bar, five halves h-bar, and so on are called fermions and described by a mathematical framework called Fermi-Dirac statistics in quantum mechanics. Particles with spin values of zero h-bar, one h-bar, two h-bar, and so on are called bosons, and are described by a mathematical framework called Bose-Einstein statistics. The quantization of spin means we have to add spins together carefully using special rules for addition of angular momentum in quantum mechanics.

In quantum mechanics, particles can also be represented mathematically using spinors. A spinor is like a vector, but instead of describing something’s size and orientation in space, it describes the particle in a theoretical space called spin space.

## Spin as a classification method

Every particle and every atom or molecule (combination of atoms) with a specific energy has its own unique spin. Thus spin is a way of classifying particles. Using spin, all particles that make up matter are fermions. For example, all quarks and leptons have spins of one-half h-bar. The particles which mediate, or convey, the fundamental forces are bosons with spins

### KEY TERMS

**Fundamental force** —A basic force, which has its own elementary mediator particle(s). There are four fundamental forces: the strong force, the electromagnetic force, the weak force, and gravity.

**Mega electron volt (MeV)** —A unit of energy. One MeV is one million Electron Volts. An Electron Volt is the amount of energy an electron gains as it passes through one Volt of potential difference.

**Quarks** —Believed to be the most fundamental units of protons and neutrons.

of one h-bar. Baryons are particles made of combinations of three quarks. They have spins of one-half h-bar or three-halves h-bar. Baryons include protons (spin one-half h-bar) and neutrons (spin one-half h-bar). Mesons are particles made of a quark and an antiquark. They have spins of zero h-bar or one h-bar.

## Isospin

Spin should not be confused with a quantum mechanical idea called isospin, isotopic spin, or isobaric spin. Isospin is the theoretical quality assigned to quarks and their combinations, which enables physicists to study the strong force that acts independently of electric charge.

## Resources

### PERIODICALS

‘Building Blocks of Matter.” *Nature*. 372 (November 1994): 20.

Lesley Smith

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## Spin of Subatomic Particles

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**Spin of Subatomic Particles**