Particles and antiparticles

Question 1

When a PET scanner is used for a brain scan:

Answer 1

A positron emitting isotope is administered to the patient and some of it reaches the brain via the blood system. Each positron emitted travels no further than a few millimetres before it meets an electron and they annihilator each other. Two gamma photons, produced as a result, are sensed bydetectors linked to computers. Gradually, an image is built up from the detector signals of where the positron-emitting nuclei are inside the brain.

Question 2

How are positron-emitting isotopes made?

Answer 2

Positron emitting isotopes do not occur naturally. They are manufactured by placing a stable isotope, in liquid or solid form, in the path of a beam of protons and become unstable positron emitters.

Question 3

Dirac’s predictions

Answer 3

• Antimatter was predicted in 1928 by English physicist Paul Dirac, before the first antiparticle, the positron, was discovered.
• Dirac predicted the existence of antimatter particles that would unlock rest energy, whenever a particle and the corresponding antiparticle met and annihilate each other.

Question 4

Einstein showed that:

Answer 4

• The mass of a particle increases the faster it travels.
• His equation E = mc² related the energy supplied to the particles to its increase in mass.
• Einstein said that the mass of a particle when it is stationary, its rest mass (m₀), corresponds to rest energy (m₀c²) locked up as mass.
• He showed that rest energy must be included in the conservation of energy.

Question 5

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

Answer 5

• annihilates the particle and itself if they meet converting their total mass into photons
• has exactly the same rest mass as particle
• has exactly opposite charge to the particle if it is charged

Question 6

Energy of a particle.

Answer 6

• The energy of a particle or antiparticle is often expressed in millions of electron volts (MeV).
• 1 MeV = 1.60 x 10^-13 J
• One electron volt is defined as the energy transferred by when an electron is moved through a pd of 1 volt.
• E=mc² can be used to work out the rest energy of a particle.

Question 7

Annihilation

Answer 7

Annihilation occurs when a particle and coresponding antiparticle meet and their mass is converted into radiation energy. Two photons are produced in this process as a single proton cannot ensure a total momentum of zero after the collision). Therefore, the minimum energy of each photon, is given by equating the energy of two photons, hf_min, to the rest energy of the particle and of the antiparticle i.e where 2hf_min = 2E₀, where E₀ is the rest energy of the particle.

Question 8

Pair production

Answer 8

• In pair production, a photon creates a particle and a corresponding antiparticle, and vanishes in the process.
• For a particle and antiparticle, each of rest E₀,

Minimum energy of a phoron needed = hf_min = 2E₀

Question 9

With a magnetic field applied to a cloud chamber, the trail of a charged particle would bend.

Answer 9

• A positive particle would be deflected by the magnetic field in the opposite direction to a negative particle travelling in the same direction.
• The slower it went, the more it would bend.

Question 10

What happens when two particles interact with each other?

Answer 10

They exert equal and opposite forces on each other and exchange momentum.

Question 11

What causes the electromagnetic repulsion between two charged particles?

Answer 11

• It is caused by the exchange of virtual photons.
• They are called virtual because they cannot be detected directly.
• If they were intercepted the force would be impeded.

Question 12

Why does the existence of a weak force needed to explain β⁺ and β^- emission.

Answer 12

• The strong force holds the protons and neutrons in the nucleus. But it does not cause protons to turn into neutrons or neutrons into protons.
• These changes can’t be due to the electromagnetic force as neutrons are uncharged particles.
• So it must be done by a force weaker than the strong force, otherwise it would affect the stability of the nuclei.

Question 13

Neutrinos and antineutrinos don’t usually interact but then these interactions take place.

Answer 13

• A neutrino can interact with a neutron and make it change into a proton. A β^- particle is created and emitted as a result of the change.
• An antineutrino can interact with a proton and make it change into a neutron. A β^{<span>+</span>} particle is created and emitted as a result of the change.
• These interactions are due to the exchange particles W bosons.

Question 14

Propery of W bosons.

Answer 14

• Non-zero mass
• A very very short range of no more than 0.001 fm
• Can be positively or negatively charged.

Question 15

In β^- decay

Answer 15

The W^- boson decays into a β^- and an antineutrino.

Question 16

Electron capture

Answer 16

• Sometimes a proton in a proton-rich nucleus turns into a neutron as a result of interacting through the weak interaction with an inner-shell electron from outside the nucleus. The W⁺ boson changes the electron into a neutrino.
• The same change can happen when a proton and an electron collide at very high speed. In addition, for an electron with sufficient energy, the overall change could also occur as a W^- exchange from the electron to the proton.

Question 17

In β​⁺ decay

Answer 17

The W⁺ boson decays into a β^{<span>+</span>} and a neutrino.