1.4 particles and antiparticles

What is annihilation?

Annihilation occurs when a particle and a corresponding antiparticle meet and their mass is converted into radiation energy. Two photons are released in the process.

What is pair production?

A photon creates a particle and a corresponding antiparticle, and vanishes in the process

Why are two photons emitted after annihilation?

One photon can not ensure a total momentum of zero after collision

Where is annihilation useful?

PET scanning is a useful application of annihilation

What is PET scanning and how does it work?

A PET scanner is used for a brain scan.

A positron emitting isotope is administered to the patient where some of it reaches the brain via the blood system

When a slow moving positron collides with a slow moving electron, they annihilate each other

As a result, 2 gamma photons are produced, detected by gamma detectors + computer builds image

When does positron emission take place?

When a proton changes into a neutron in an unstable nucleus with too many protons

During positron emission, a positron is emitted. What other particle is emitted?

A neutrino

Positron emission isotopes do not occur naturally. How are they manufactured?

By placing an isotope (liquid or solid) in the path of a beam of protons.

This works because some of the nuclei in the substance absorb extra protons and become unstable positron emitters (positron emission takes place when a proton changes into a neutron in an unstable nucleus with too many protons).

Dirac’s theory

Dirac’s theory of antiparticles predicted that for every type of particle there is a corresponding antiparticle that:

• annihilates the particle and itself if they meet, converting their total mass into photons

• Has exactly the same rest mass as the particle

• Has exactly opposite charge to the particle if the particle has a charge

What is rest mass?

Mass of a particle when stationary

Dirac’s prediction of pair production

Dirac predicted that a photon with sufficient energy passing near a nucleus or an electron can suddenly change into a particle/antiparticle pair, which would then separate from each other.

How is E=mc² and annihilation linked?

Einstein had shown that the mass of a particle increases the faster it travels (E=mc² relates the energy supplied to the particle to its increase in mass)

Einstein said that the rest mass (m₀), corresponds to rest energy (m₀c²) locked up as mass. Dirac predicted that the existence of antiparticles would unlock the rest energy whenever a particle and corresponding antiparticle would collide + annihilate each other.

What unit is the energy of a particle/antiparticle expressed in?

Millions of electron volts (MeV)

What is 1MeV in joules?

1MeV = 1.60 × 10^-13 Joules

What is the definition of an electron volt?

The energy transferred when an electron is moved through a potential difference of 1 volt

In annihilation, what is the minimum energy of the photons?

2hf (because there are 2 photons)

2hf = 2m₀c² = 2E₀ (Dirac said that annihilation of particles and antiparticles unlock rest energy, so energy of two photons is equivalent to rest energy of particle and antiparticle

In pair production, what is the energy needed for photon?

The minimum energy needed for a photon =

hf (minimum) = 2E₀

(Only hf not 2hf as there is only one photon)

(2E₀ not just E₀ as a particle and an antiparticle have been created)

If an electron has a rest energy (E₀) of 0.511 MeV, what was the minimum energy of the photon that produced this electron and its corresponding antiparticle?

2 × 0.511 MeV = 1.022 MeV (we multiple by two as a particle’s corresponding antiparticle has exactly the same rest mass and so exactly the same rest energy according to Dirac)

1.022 MeV = 1.64 × 10^-13 (remember 1 MeV = 1.60 × 10^-13 J)