Nuclear instability (A-level only) — AQA A-Level Physics

Nuclear instability explains why some atomic nuclei are unstable and undergo radioactive decay. You will study the four main types of decay (alpha, beta-minus, beta-plus and gamma), the changes they cause in the nucleus, and how to represent them with balanced nuclear equations. The topic also introduces the N-Z graph, which shows how the ratio of neutrons to protons determines the stability of a nucleus and predicts the likely mode of decay.

This topic is fundamental to understanding radioactivity, nuclear energy and medical physics. It builds on your knowledge of atomic structure and the strong nuclear force from earlier in the A-level course. Exam questions often require you to apply conservation laws, interpret decay equations, and perform calculations involving activity, decay constant and half-life, making it a key area for both mathematical and explanatory skills.

• →Alpha decay emits a helium nucleus (4/2 He), reducing the nucleon number by 4 and the proton number by 2. Beta-minus decay emits an electron and an antineutrino, increasing the proton number by 1. Beta-plus decay emits a positron and a neutrino, decreasing the proton number by 1. Gamma emission releases excess energy without changing the nucleon or proton number.
• →The N-Z graph plots neutron number against proton number for stable nuclides. The line of stability shows that light stable nuclei have N approximately equal to Z, while heavier stable nuclei have N greater than Z. Nuclei above the line are neutron-rich and undergo beta-minus decay; those below are proton-rich and undergo beta-plus decay or electron capture.
• →Conservation laws in nuclear decay: nucleon number (mass number) and charge (proton number) must be conserved in all nuclear equations. Lepton number is also conserved, which is why neutrinos and antineutrinos are included in beta decay equations.
• →The activity A of a radioactive source is the number of decays per second, measured in becquerels (Bq). Activity decreases exponentially with time: A = A0 e^(-lambda t), where lambda is the decay constant. The decay constant is related to half-life by lambda = ln(2) / t_half.
• →The number of undecayed nuclei N also decreases exponentially: N = N0 e^(-lambda t). The activity is proportional to the number of undecayed nuclei, so A = lambda N.

• Plot N on the vertical axis and Z on the horizontal axis, with stable nuclei forming a narrow curved band.
• State that light stable nuclei have N approximately equal to Z, giving a ratio close to 1.
• Explain that heavier stable nuclei need a higher N/Z ratio, up to about 1.5, because of increasing Coulomb repulsion between protons.
• Identify neutron-rich nuclei above the band as likely beta-minus emitters and proton-rich nuclei below the band as likely beta-plus emitters or electron capturers.
• Relate alpha emission of very heavy nuclei to overall instability beyond Z = 83, noting that beta decays also occur in heavy decay chains.
• Use the graph to predict a likely decay mode for a given nuclide from its position relative to the band.
• Alpha emission removes two protons and two neutrons, so the daughter nuclide has Z decreased by 2 and N decreased by 2, with mass number A decreased by 4.
• Beta-minus decay changes a neutron into a proton, so Z increases by 1 and N decreases by 1 while A stays constant; an electron and an antineutrino are emitted.
• Beta-plus decay changes a proton into a neutron, so Z decreases by 1 and N increases by 1 while A stays constant; a positron and a neutrino are emitted.
• Electron capture combines an inner-shell electron with a proton to form a neutron, so Z decreases by 1 and N increases by 1 while A stays constant; a neutrino is emitted.
• The N-Z plot shows that neutron-rich nuclides tend to undergo beta-minus decay, proton-rich nuclides tend to undergo beta-plus decay or electron capture, and heavy nuclides tend to undergo alpha emission.
• In alpha decay, the equation shows the parent nuclide producing a daughter with A decreased by 4 and Z decreased by 2, plus a ⁴₂He particle.
• In beta-minus decay, the equation shows the parent nuclide producing a daughter with Z increased by 1 and A unchanged, plus an electron and an antineutrino.
• In beta-plus decay, the equation shows the parent nuclide producing a daughter with Z decreased by 1 and A unchanged, plus a positron and a neutrino.
• In electron capture, the equation shows the parent nuclide combining with an electron to produce a daughter with Z decreased by 1 and A unchanged, plus a neutrino.
• Conservation of A and Z must hold on both sides of every decay equation.
• States that a nucleus can exist in excited states after alpha or beta decay, with energy above the ground state.
• Describes gamma emission as a photon emitted when the nucleus drops to a lower energy state, with no change in proton or nucleon number.
• Explains that gamma photons are electromagnetic radiation with no mass and no charge, so they are highly penetrating.
• Describes technetium-99m as a metastable gamma-emitting source used as a medical tracer.
• Explains that the gamma radiation is detected outside the body to reveal the distribution of the tracer in an organ.
• Links the roughly six-hour half-life to a useful balance between sufficient activity for imaging and a limited radiation dose to the patient.
• Recognises that a suitable tracer must also be non-toxic and follow a known biological pathway to the target organ.

• 💡Sketch the axes with N vertical and Z horizontal and label the line of stability before adding any nuclide.
• 💡Quote the approximate stable N/Z ratio for light and heavy nuclei to support your explanation.
• 💡When predicting decay, state whether the nuclide is above or below the band and name the decay mode that moves it towards the band.
• 💡Write the parent and daughter nuclides with correct A and Z before balancing any decay equation.
• 💡Check conservation of A and Z after every decay to confirm the mode is consistent.
• 💡Use the N-Z plot to justify why a particular nuclide decays by one mode rather than another.
• 💡Balance A and Z separately before checking the particle emitted.
• 💡Use the periodic table or data sheet to confirm the chemical symbol of the daughter nuclide.
• 💡Include the neutrino or antineutrino in beta and electron capture equations where required.
• 💡Use the term metastable when describing technetium-99m, and quote its half-life as approximately six hours.
• 💡When explaining medical use, structure the answer as uptake, gamma emission, external detection and image formation.
• 💡State explicitly that gamma emission leaves proton and nucleon numbers unchanged, since this is a common discriminator in mark schemes.
• 💡Link the short half-life to patient safety and to practical imaging time rather than listing it without comment.
• 💡Mention one named organ or application, such as heart, bone or kidney imaging, to make the application concrete.
• 💡Always balance nuclear equations for both nucleon number (top) and proton number (bottom). Include the neutrino or antineutrino in beta decay equations to conserve lepton number; omitting them loses marks.
• 💡When using exponential decay equations, convert half-life to seconds and ensure time is in seconds. Show your value of the decay constant to at least 3 significant figures before calculating the final answer.
• 💡For 'explain' questions about stability, refer explicitly to the neutron-to-proton ratio and the balance between the strong nuclear force and electrostatic repulsion. Use the N-Z graph to justify your answer.

• Assuming the line of stability is straight with N = Z for all nuclei; correction: it curves upwards so heavy stable nuclei have more neutrons than protons.
• Thinking that any nucleus with N greater than Z is unstable; correction: many light stable nuclei have N slightly greater than Z, and stability depends on the position relative to the band.
• Assuming heavy nuclei (Z > 83) only decay by alpha emission; correction: while alpha decay reduces overall mass, heavy nuclei also undergo beta decay to correct their N/Z ratio during decay chains.
• Treating beta-minus decay as loss of an electron from the nucleus; the correction is that a neutron transforms into a proton and the emitted electron is created in the decay.
• Confusing beta-plus decay with electron capture because both lower Z by 1; the correction is that beta-plus emits a positron while electron capture absorbs an inner electron.
• Assuming alpha emission changes only Z; the correction is that both Z and N fall by 2 and A falls by 4.
• Writing a beta-minus decay equation without the antineutrino; the correction is to include the antineutrino so lepton number is conserved.
• Changing A during beta decay; the correction is that A remains constant because only a neutron-proton conversion occurs.
• Omitting the electron in an electron capture equation; the correction is to show the captured electron on the left-hand side.
• Saying gamma emission changes the element: correct this by stating that gamma emission alters neither proton number nor nucleon number, so the nuclide stays the same.
• Confusing gamma rays with alpha or beta particles: correct this by describing gamma as uncharged electromagnetic radiation with no mass, unlike charged, massive alpha and beta emissions.
• Claiming technetium-99m is a stable or permanent source: correct this by describing it as metastable, decaying by gamma emission with a half-life of about six hours.
• Treating the gamma photons as the imaging agent itself: correct this by explaining that the tracer is taken up by the organ and the emitted gamma photons are detected externally.
• Students often think that beta particles come from the electron shells of the atom. In fact, beta-minus particles are created in the nucleus when a neutron transforms into a proton, and beta-plus particles are created when a proton transforms into a neutron.
• Many students believe that gamma decay changes the element. Gamma emission only releases excess energy as a photon; it does not change the proton number or nucleon number, so the element remains the same.
• Students sometimes assume that after one half-life, all nuclei have decayed. In reality, half-life is a statistical concept: after one half-life, half of the original nuclei remain undecayed, but individual decay events are random.

1. 1Day 1-2: Review atomic structure and the strong nuclear force. Learn the definitions of alpha, beta-minus, beta-plus and gamma decay, and practise writing balanced nuclear equations for each type.
2. 2Day 3-4: Study the N-Z graph and the line of stability. For each region (above, below, and on the line), identify the likely decay mode and explain why in terms of the neutron-to-proton ratio.
3. 3Day 5-6: Learn the equations for activity and number of nuclei: A = A0 e^(-lambda t), N = N0 e^(-lambda t), lambda = ln(2)/t_half, and A = lambda N. Practise calculations with different time units.
4. 4Day 7-8: Complete past-paper questions on nuclear instability, focusing on 4-6 mark explanations and calculations. Mark your answers using the mark scheme and note recurring errors.
5. 5Day 9-10: Create a summary sheet with all key equations, decay types, and graph features. Test yourself with active recall prompts and flashcards, then attempt a timed exam-style question under pressure.

• 📋Nuclear equation completion: You are given a decay equation with a missing particle or daughter nucleus and must balance nucleon and proton numbers. Advice: always check both top and bottom numbers, and remember to include neutrinos/antineutrinos for beta decay.
• 📋Calculation of activity or number of nuclei after a given time: You may need to find the decay constant from half-life, then use A = A0 e^(-lambda t) or N = N0 e^(-lambda t). Advice: convert all times to seconds and show your working clearly.
• 📋Explain why a particular nucleus is unstable and predict its decay mode: You must refer to the N-Z graph and the neutron-to-proton ratio. Advice: use precise terms like 'neutron-rich' or 'proton-rich' and link to the specific decay process.
• 📋Graph interpretation: You may be asked to identify a decay from an N-Z graph or sketch the position of a daughter nucleus. Advice: remember that alpha decay moves the nucleus down and left by 2 protons and 2 neutrons; beta-minus moves it up and left (Z increases by 1, N decreases by 1).