Matter

1
Matter Radiation 4Particles and antiparticles

• Unit 1.1a4
• Breithaupt chapter 1.4
• pages 10 to 12

2
AS specification

• Candidates should know that for every type of
  particle, there is a corresponding antiparticle.
  They should know that the positron, the
  antiproton, the antineutron and the antineutrino
  are the antiparticles of the electron, the
  proton, the neutron and the neutrino
  respectively.
• Comparison of particle and antiparticle masses,
  charge and rest energy in MeV.
• Knowledge of annihilation and pair production
  processes and the respective energies involved.
  The use of E mc2 is not required in
  calculations.

3
Antimatter

• Most particles of normal matter, such as protons,
  neutrons and electrons have a corresponding
  particle that
• has the same mass
• has opposite charge (if the normal particle is
  charged)
• will undergo annihilation with the normal
  particle if they meet
• Examples
• an antiproton is negatively charged
• an anti-electron, normally called a positron, has
  a positive charge

LHC Rap
4
Further notes on antimatter

• Other particle properties are also reversed in
  antimatter allowing the existence of uncharged
  antiparticles such as the antineutron.
• Two particles that have the same mass and
  opposite charges are not necessarily a particle
  and an antiparticle pair.
• The antineutrino produced in beta-minus decay is
  an example of antimatter.
• Most examples of antimatter have a symbol that
  adds a bar above the normal matter symbol e.g.
• Certain man-made isotopes are made in order to
  provide a source of antimatter. e.g. positrons
  are needed for PET scans (see page 10).

5
Annhilation

• When a particle and its corresponding
  antiparticle meet together annihilation occurs.
• All of their mass and kinetic energy is converted
  into two photons of equal frequency that move off
  in opposite directions.

6
Pair production

• The opposite of annihilation.
• The energy of one photon can be used to create a
  particle and its corresponding antiparticle.
• The proton ceases to exist afterwards

7
The electron-volt (eV) and MeV

• The electron-volt (symbol eV) is a very small
  unit of energy equal to 1.6 x 10-19 J
• The electron-volt is equal to the kinetic energy
  gained by an electron when it is accelerated by a
  potential difference of one volt
• Also 1 MeV (megaelectron-volt) 1.6 x 10-13 J
• Question Calculate the energy in electron-volts
  of a photon of orange light of frequency 4.5 x
  1014 Hz
• E h x f (6.63 x 10-34 Js) x (4.5 x 1014 Hz)
• 2.98 x 10-19 J
• energy in eV energy in joules / 1.6 x
  10-19
• 1.86 eV

8
Particle rest energy

• Using Einsteins relation E mc2 the energy
  equivalent of mass can be calculated. The masses
  of sub-atomic particles are commonly quoted in
  energy terms using the unit MeV.
• Example the mass of a proton is 1.67 x 10-27 kg
• E mc2 (1.67 x 10-27 kg) x (3.0 x 108 ms-1)2
• 1.50 x 10-10 J
• This is normally expressed in terms of MeV where
  1 MeV 1.6 x 10-13 J
• And so the mass-energy of a proton in MeV (1.50
  x 10-10 J) / (1.6 x 10-13 J)
• 938 MeV
• This will be the energy of a stationary proton
  having no kinetic energy and as such is referred
  to as the rest energy of a proton
• Other (and more precise) rest energies in MeV
  (from page 245)
• proton 938.257 neutron 939.551 electron
  0.510999 photon 0
• Mass is sometimes quoted using the unit GeV/c2
  (1000 MeV/c2 1 GeV/c2 )
• for example proton rest mass 0.938 GeV/c2

9
Annihilation calculation

• Calculate the minimum energies of the photons
  produced by the annihilation of a proton and
  antiproton.
• The minimum energies occur when the pair of
  particles have initially insignificant kinetic
  energy.
• rest energy of a proton in MeV 938MeV
• rest energy of an antiproton also 938MeV
• total mass converted into electromagnetic
  radiation in the form of two photons 1876 MeV
• therefore each photon has an energy of 938 MeV
• Further question What would be the wavelength of
  these photons?
• 938MeV 1.50 x 10-10 J
• E hc / ? becomes ? E / hc
• and so ? (1.50 x 10-10 J) / ((6.63 x 10-34 Js)
  x (3.0 x 108 ms-1))
• 7.54 x 10-18 m (gamma radiation)

10
Pair production calculation

• Calculate the minimum photon energy required to
  produce an electron-positron pair.
• The minimum energy will produce two stationary
  particles (which would then annihilate each other
  again!)
• rest energy of an electron in MeV 0.511 MeV
• rest energy of a positron also 0.511MeV
• therefore minimum energy required 2 x 0.511
• 1.022 MeV
• Further question What would be the frequency of
  this photon?
• 1.022 MeV 1.64 x 10-13 J
• E hf becomes f E / h
• and so f (1.64 x 10-13 J) / (6.63 x 10-34 Js)
• 2.47 x 1020 Hz (gamma radiation)

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Notes from Breithaupt pages 10 to 12

• What is anitimatter? How does antimatter compare
  in mass and charge with normal matter?
• State what is meant by annihilation and
  pair-production in the context of antimatter.
• What is (a) an electron-volt (b) MeV?
• Explain how the rest energy of a proton can be
  stated as 938MeV
• Explain why a photon must have a minimum energy
  of 1.022MeV in order to produce an
  electro-positron pair.
• How was the positron first discovered? How are
  positrons used in PET scans?
• Try the summary questions on page 12

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Answers to the summary questions