Particle physics

• Top numbers and bottom numbers balance in every equation; β− brings an antineutrino and turns d into u, β+ brings a neutrino and turns u into d.
• Most through, few deflected, very few back. Top and bottom balance. β−: d → u with an antineutrino; β+: u → d with a neutrino. u, c, t +⅔; d, s, b −⅓.

• 11.1.1 I can — infer from the results of the α-particle scattering experiment the existence and small size of the nucleus
• 11.1.2 I can describe — describe a simple model for the nuclear atom to include protons, neutrons and orbital electrons
• 11.1.3 I can — distinguish between nucleon number and proton number
• 11.1.4 I can understand — understand that isotopes are forms of the same element with different numbers of neutrons in their nuclei
• 11.1.5 I can understand — understand and use the notation AZX for the representation of nuclides
• 11.1.6 I can understand — understand that nucleon number and charge are conserved in nuclear processes
• 11.1.7 I can describe — describe the composition, mass and charge of α-, β- and γ-radiations (both β– (electrons) and β+ (positrons) are included)
• 11.1.8 I can understand — understand that an antiparticle has the same mass but opposite charge to the corresponding particle, and that a positron is the antiparticle of an electron
• 11.1.9 I can state — state that (electron) antineutrinos are produced during β– decay and (electron) neutrinos are produced during β+ decay
• 11.1.10 I can understand — understand that α-particles have discrete energies but that β-particles have a continuous range of energies because (anti)neutrinos are emitted in β-decay
• 11.1.11 I can — represent α- and β-decay by a radioactive decay equation of the form ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α
• 11.1.12 I can use — use the unified atomic mass unit (u) as a unit of mass
• 11.2.1 I can understand — understand that a quark is a fundamental particle and that there are six flavours (types) of quark: up, down, strange, charm, top and bottom
• 11.2.2 I can recall — recall and use the charge of each flavour of quark and understand that its respective antiquark has the opposite charge (no knowledge of any other properties of quarks is required)
• 11.2.3 I can recall — recall that protons and neutrons are not fundamental particles and describe protons and neutrons in terms of their quark composition
• 11.2.4 I can understand — understand that a hadron may be either a baryon (consisting of three quarks) or a meson (consisting of one quark and one antiquark)
• 11.2.5 I can describe — describe the changes to quark composition that take place during β– and β+ decay
• 11.2.6 I can recall — recall that electrons and neutrinos are fundamental particles called leptons

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “β+ decay emits an antineutrino.” Correct β− gives an antineutrino; β+ gives a neutrino. The electron (a particle) is paired with the antineutrino (an antiparticle); the positron (an antiparticle) is paired with the neutrino (a particle).
• “Most of the α-particles bounced back off the gold foil.” Correct Almost all went straight through. Only a very small fraction were deflected through more than 90°, and it is their rarity that shows the nucleus is small.
• “The β− particle is one of the atom's orbital electrons.” Correct It is created in the nucleus at the moment of decay, when a neutron becomes a proton (a down quark becomes an up quark).
• “β-particles have a range of energies because they lose energy on the way out of the source.” Correct Each decay shares its energy between the β-particle and an (anti)neutrino, in a different proportion every time. That is the syllabus's reason, and the only one to give.
• “The down quark has charge −⅔e.” Correct u, c and t have +⅔e; d, s and b have −⅓e. Check with the neutron: udd must total 0.
• “A meson is two quarks.” Correct A meson is one quark and one antiquark. Two quarks alone are neither a baryon nor a meson.
• “An antiparticle is the opposite of the particle in every way.” Correct Same mass, opposite charge. Both halves are part of the definition: a proton and an electron have opposite charges but are not each other's antiparticles.
• “The large deflections show that the nucleus is negative, because it attracts the α-particles.” Repair The α-particles are positive and are repelled: every path bends away from the nucleus. The nucleus is positive (11.1.1).
• “The foil is thin so that the α-particles can get through it.” Repair It is thin so that each α-particle is scattered by at most one nucleus; a large deflection is then one close encounter, not many small ones added together (11.1.1).
• “Isotopes have different numbers of protons.” Repair Isotopes are forms of the same element, so the same number of protons, with different numbers of neutrons (11.1.4).
• “The nucleon number of an electron is 0, so an electron has no mass.” Repair The top number counts nucleons, not mass. An electron contains no nucleons but has mass 9.11 × 10−31 kg (11.1.5).
• “The number of protons is conserved in every nuclear process.” Repair Charge is conserved, and nucleon number. In β− decay the proton count rises by one; the electron created keeps the total charge the same (11.1.6).
• “\({}^{14}_{6}\mathrm{C} \to {}^{14}_{7}\mathrm{N} + {}^{0}_{-1}\beta\) balances, so that is the whole decay.” Repair An antineutrino, \({}^{0}_{0}\bar{\nu}\), is also emitted. It changes neither total, but it is part of the decay and the reason the β energies are continuous (11.1.9).
• “A γ emission changes the nucleon number by 0 and the proton number by 0, so it turns the nucleus into a different nuclide of the same element.” Repair Same A and same Z means the same nuclide. γ emission only lowers the energy of an excited nucleus (11.1.7).
• “1 u is the mass of a proton.” Repair 1 u is one-twelfth of the mass of a carbon-12 atom, 1.66 × 10−27 kg. A proton is 1.01 u (11.1.12).
• “In β− decay a neutron's up quark turns into a down quark.” Repair The reverse. β−: d → u (udd becomes uud). β+: u → d. Check the charge: a neutron can only become positive if a −⅓e quark becomes a +⅔e one (11.2.5).
• “The antiquark of the down quark has charge −⅓e, because it is the anti-down.” Repair An antiquark has the opposite charge: d̄ is +⅓e (11.2.2).
• “Electrons and protons are both fundamental particles.” Repair The electron is a fundamental lepton. The proton is a baryon made of three quarks, uud, so it is not fundamental (11.2.6).
• “The positron is a hadron, because it comes out of the nucleus.” Repair A hadron is made of quarks. The positron is not; it is the antiparticle of the electron, an antilepton, created in the decay (11.2.4).

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Interleave with the chapters that use this one. When you reach topic 22 (quantum physics), re-answer: why are α energies discrete? When you reach topic 23 (nuclear physics), rewrite worked example 2 and ask what the equations leave out. When you reach topic 24 (medical physics), describe the β+ decay and the positron again before learning what the positron does next. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 11 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• A Paper 1 item on this topic can turn on a single fact held precisely: which observation shows which property of the nucleus, which particle goes with β+, the charge of a strange quark, whether a combination is a baryon or a meson, the missing particle in a decay. A Paper 2 question can ask you to describe the scattering results and explain what they show, to state the composition, mass and charge of a radiation, to explain the continuous β spectrum, and to describe a quark change with a charge check.
• Numbers of protons, neutrons and electrons; nuclear charge Ze; masses from A u with 1 u = 1.66 × 10−27 kg; the missing particle in an equation; the charge of a hadron from its quarks; the speed of an α-particle from its kinetic energy; the share of a β decay's energy taken by the (anti)neutrino. The Data sheet gives e, u, mp and me; the quark charges, N = A − Z and the conservation rules are recall. The one graph is a sketch of the β energy spectrum.
• The syllabus names no experiment for this topic, and Paper 5 may set a radioactive context with the data supplied. The skills are background counting and subtraction, repeated counts with an uncertainty of half the range, identifying a radiation from absorbers, and, as a Paper 5-style item, linearising the inverse-square law for γ radiation to find an unknown distance from a graph with error bars and a worst acceptable line.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.