WJEC Physics for AS: Student Bk

81 Terms & definitions Terms & definitions Particles and nuclear structure Particle masses are also expressed in a combination of energy units and the speed of light c , using the Einstein relationship, E = mc 2 . Rearranging this gives m = E c 2 , which allows us to write the mass of a particle in the unit eV / c 2 . In these units, the electronic mass, m e is 0.511 MeV c 2 . The conversion to SI units proceeds as follows: m e = 0.511 MeV c 2 = 0.511 × 1.602 × 10 –13 J ( 2.998 × 10 8 m s –1 ) 2 = 9.11  ×  10 –31 kg . 1.7.3 Antiparticles Antimatter is not only the stuff of science fiction. For each of the particles in Table 1.7.1, there is corresponding antiparticle with an identical mass; if the particle has a charge, the antiparticle has an equal and opposite charge. The symbol for most antiparticles that you will meet is formed by putting a bar over the symbol for the particle, e.g.  u ,  ν e ,  p for the anti-up quark, the electron antineutrino [or ‘anti-electron neutrino’] and the antiproton respectively. The exceptions are the antiparticles of the electron, muon and tauon which are written e + , μ + and τ + respectively. The antielectron has its own name: the positron . When a particle and its antiparticle interact they annihilate each other; that is they disappear and their mass-energy manifests itself as two photons of electromagnetic radiation. These photons are given the symbol g because they are at the very high energy end of the e-m spectrum. The total energy of the photons is equal to the sum of the mass- energy and kinetic energy of the annihilating particles. Example An electron and a positron collide head on and annihilate. Each particle has a kinetic energy of 100 keV . Calculate the energy of each of the photons produced. Answer Electron mass = 511 keV / c 2 , so the mass energy is 511 keV . ∴ Total energy = total mass energy + total kinetic energy = 2 × 511 keV + 2 × 100 keV = 1222 keV ∴ Each photon has energy ½ × 1222 keV = 611 keV Examtip The WJEC specification requires knowledge that there are three generations of particles but questions involving interactions will be restricted to the first. Tab. 1.7.1 Standard model particles Generation Leptons Quarks 1st electron Symbol: e - charge: - e electron neutrino Symbol: ν e charge: 0 up Symbol: u charge: 2 3 e down Symbol: d charge: – 1 3 e 2nd muon Symbol: μ - charge: - e muon neutrino Symbol: ν μ charge: 0 charm Symbol: c charge: 2 3 e strange Symbol: s charge: – 1 3 e 3rd tauon Symbol: τ - charge: - e tauon neutrino Symbol: ν τ charge: 0 top Symbol: t charge: 2 3 e bottom Symbol: b charge: – 1 3 e The elementary charge , e , is the charge on the proton and has a value of 1.602 × 10 –19  C (4 s.f.). The charge on the electron is – e . The electron volt is the energy transfer when an electron moves through a potential difference of one volt. Using the definition of a volt, W = QV , ∴ 1 eV = 1.602 × 10 –19 J Also 1 keV = 1.602 × 10 –16 J and 1 MeV = 1.602 × 10 –13 J 1.7.1 Self-test To convert from MeV / c 2 to kg we multiply by 10 6 e and divide by c 2 . Invert this method to express the proton mass of 1.672 × 10 –27 kg in GeV / c 2 . Study point If an electron and a positron annihilate, they produce two g photons. These are emitted in opposite directions – otherwise momentum would not be conserved. 1.7.2 Self-test Calculate the wavelength, frequency and momentum of the photons in the example. [See Section 2.7 for the momentum of a photon.]