HSC Exam Practice

Sample response. An antiparticle is a particle with the same rest mass as its corresponding particle but opposite charge and opposite quantum numbers (baryon number, lepton number). Two distinguishing properties: (1) opposite electric charge (e.g. the positron has charge +1e vs the electron’s −1e); (2) opposite baryon or lepton number (e.g. an antiproton has baryon number −1 vs the proton’s +1). When a particle meets its antiparticle, they annihilate, converting rest-mass energy to photons or other particle–antiparticle pairs.

Marking notes. 1 mark for a definition including “same rest mass but opposite charge / quantum numbers”; 1 mark for a correctly stated first distinguishing property with example; 1 mark for a correctly stated second distinguishing property with example.

Sample response. When an electron and a positron are approximately at rest, the total initial momentum of the system is zero. Conservation of momentum requires the total momentum of the products to also be zero. A single photon cannot have zero momentum (since all photons carry momentum p = E/c ≠ 0). Two photons emitted in exactly opposite directions each carry equal and opposite momenta that sum to zero, satisfying conservation of momentum. Conservation of energy is also satisfied: E_total = 2m_ec² = 2 × 0.511 MeV = 1.022 MeV, shared equally between the two photons.

Marking notes. 1 mark for stating that total initial momentum is zero (at rest); 1 mark for explaining that a single photon cannot have zero momentum, so two are required; 1 mark for explaining that two opposite-direction photons satisfy both momentum and energy conservation.

Sample response. Hadrons are composite particles made of quarks that experience the strong nuclear force; they have a measurable internal structure. Leptons are fundamental (point-like) particles that do not experience the strong nuclear force and have no known substructure. The proton is a hadron: it is made of three quarks (uud) and participates in strong interactions. The electron is a lepton: it has no quark content, does not experience the strong force, and carries lepton number +1.

Marking notes. 1 mark for correct distinction between hadrons (quark composites, strong force) and leptons (fundamental, no strong force); 1 mark for correctly classifying the proton as a hadron with justification (made of quarks / strong force); 1 mark for correctly classifying the electron as a lepton with justification (fundamental / no strong force); 1 mark for precise terminology (baryon / meson distinction, lepton number, or quark content of proton).

Sample response. Pair production requires the photon energy to be at least equal to the combined rest-mass energy of the particle–antiparticle pair. E_min = 2m_pc² = 2 × 938.3 MeV = 1876.6 MeV ≈ 1.877 GeV. A photon of at least 1876.6 MeV is required near a nucleus (which absorbs the recoil momentum).

Marking notes. 1 mark for correctly stating E_min = 2m_pc²; 1 mark for correct substitution (2 × 938.3 MeV); 1 mark for correct answer 1876.6 MeV (accept 1876 MeV or 1.877 GeV). Deduct 1 mark if the student uses the electron mass (0.511 MeV) instead of the proton mass.

Sample response. The neutron consists of one up quark and two down quarks (udd). Quark charges: up quark = +⅔e; down quark = −⅓e. Total charge = +⅔ − ⅓ − ⅓ = 0. The individual fractional quark charges cancel exactly to give the neutron its zero electric charge.

Marking notes. 1 mark for correct quark composition (udd); 1 mark for correctly stating quark charges (+⅔ for up, −⅓ for down); 1 mark for showing the arithmetic sum is zero and explicitly linking this to the neutron’s zero charge.

Sample response. A free neutron decays (n → p + e⁻ + ν̄_e) because its rest mass is greater than the combined rest mass of the proton and electron: m_nc² = 939.6 MeV > m_pc² + m_ec² = 938.8 MeV. This mass difference (~0.8 MeV) is released as kinetic energy of the products, so the decay is energetically permitted. A free proton cannot decay into a neutron by the same route because the proton has lower rest mass than the neutron; the reverse decay would violate conservation of energy. Additionally, baryon number is conserved in both cases (B = 1 on both sides), and lepton number is conserved by the antineutrino accompanying the electron.

Marking notes. 1 mark for identifying that the neutron has greater rest mass than the proton, making decay energetically favourable; 1 mark for explaining that the proton cannot decay into a neutron because it would require an increase in rest mass (violation of conservation of energy without additional input); 1 mark for referencing a relevant conservation law (baryon number or energy conservation) correctly applied to both cases.

Sample response (a). Both tracers produce annihilation photons of 0.511 MeV each. This equals the rest mass energy of an electron (or positron): E = m_ec² = 0.511 MeV [1]. Both tracers produce the same photon energy because, in the common clinical situation, the positrons thermalise (lose their kinetic energy to the surrounding tissue) before annihilating. By the time annihilation occurs, the positron and electron are both essentially at rest [1]. Conservation of energy then gives each photon exactly m_ec² = 0.511 MeV regardless of the original positron kinetic energy [1].

Sample response (b). The positron enters with kinetic energy K_e+ = 0.634 MeV and the electron is at rest (KE = 0). The electron also contributes its rest-mass energy m_ec² = 0.511 MeV. By conservation of energy, total energy of annihilation photons = rest-mass energy of both particles + kinetic energy of positron = 0.511 (positron rest) + 0.511 (electron rest) + 0.634 (positron KE) = 1.656 MeV. So the two photons together carry 1.656 MeV [1 for method; 1 for substitution; 1 for correct answer 1.656 MeV].

Sample response (c). In practice, positrons from the ¹⁸F decay travel only a few millimetres in tissue before being slowed to near rest by multiple ionisation interactions with tissue electrons [1]. Only when the positron has effectively thermalised does it annihilate with a tissue electron. Because most of the positron’s initial kinetic energy has been deposited in tissue before the annihilation event, the annihilation itself proceeds from a near-at-rest state, and the photons have energies close to 0.511 MeV [1]. The slight residual momentum of the electron–positron pair at the moment of annihilation causes a small Doppler shift and Doppler broadening of the 0.511 MeV peak, but this shift is too small (a few keV) to be clinically significant [1].

Marking notes. Part (a): 1 = states both tracers give 0.511 MeV and links to m_ec²; 1 = explains thermalisation of positron before annihilation; 1 = links each photon energy to m_ec² via energy conservation. Part (b): 1 = correct setup including rest-mass energies of both particles; 1 = correct substitution with units; 1 = correct total 1.656 MeV. Part (c): 1 = explains that positron thermalises by ionisation loss in tissue before annihilating; 1 = links thermalisation to near-at-rest annihilation and hence 0.511 MeV photons; 1 = notes residual Doppler broadening is small (or equivalent: recognises that residual kinetic energy at annihilation is negligible).

Sample response. Dirac’s relativistic quantum equation (1928) predicted that for every spin-½ fermion there must exist an antiparticle with equal mass but opposite charge and quantum numbers. Carl Anderson’s 1932 cloud chamber observation of the positron was the first direct experimental confirmation: the track curvature in a magnetic field showed a particle with the electron’s mass but positive charge, matching Dirac’s prediction precisely. Subsequent experiments identified the antiproton (1955, Emilio Segrè, at the Bevatron), antineutron, and eventually antihydrogen (CERN ALPHA experiment), providing compelling evidence that antiparticles exist for all known particles and that antimatter obeys the same physical laws.

Conservation laws are central to determining which interactions are possible. Charge conservation (Q) forbids processes that change total electric charge; for example, a proton cannot decay to a positron and a neutrino alone because B = +1 on the left but B = 0 on the right. Baryon number conservation prevents the spontaneous disappearance of baryons: the proton is stable because any decay product set with B = +1 would require at least one baryon in the products, but no lighter baryon exists. Lepton number conservation (separately for each lepton family) constrains beta decay: neutron decay n → p + e⁻ + ν̄_e conserves electron lepton number (L_e: 0 = 0 + 1 + (−1) = 0); omitting the antineutrino would violate L_e and is never observed. Energy and momentum conservation together require that electron–positron annihilation at rest produces exactly two opposite-directed photons of 0.511 MeV each, not one.

The matter–antimatter asymmetry is one of the deepest unsolved problems in physics. The Big Bang should have produced equal amounts of matter and antimatter. If they had annihilated completely, the universe would contain only photons — yet we observe a universe dominated by matter. The small asymmetry (approximately one extra matter particle for every billion matter–antimatter pairs) means that CP violation (a subtle difference in the laws governing matter and antimatter, first observed in kaon decay by Cronin and Fitch, 1964) must have operated in the early universe to produce a net surplus of quarks over antiquarks. This relic matter surplus is all the matter we see today. The Standard Model’s current level of CP violation is too small by orders of magnitude to explain the observed asymmetry, pointing to physics beyond the Standard Model as an active research frontier.

Marking criteria (8 marks). 1 = describes Dirac’s prediction and states that it required an antiparticle for every fermion with equal mass and opposite quantum numbers. 1 = names Anderson’s positron discovery (1932) as the first experimental confirmation, with at least one detail (cloud chamber, charge sign, mass). 1 = names a second experimental confirmation (antiproton, antineutron, or antihydrogen) with correct context. 1 = correctly explains how at least two specific conservation laws (from: charge, B, L, energy, momentum) constrain which interactions are possible, with a named example for each law. 1 = second conservation law correctly discussed with example. 1 = explains the matter–antimatter asymmetry problem (equal creation in Big Bang; annihilation leaving only photons if symmetric; observed matter-dominated universe). 1 = links CP violation (or a correctly described asymmetry mechanism) to the observed surplus of matter. 1 = reaches an explicit evaluative statement integrating Dirac’s prediction, the experimental evidence, and the unresolved question of the matter–antimatter asymmetry as evidence for physics beyond the Standard Model.