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    Radioactive decay (A-level only) — AQA A-Level Physics

    Teaching note checked against the official specification.

    Radioactive decay is the spontaneous and random disintegration of unstable atomic nuclei, emitting alpha, beta or gamma radiation to become more stable. AQA A-Level Physics requires you to apply the exponential decay equation, define activity and half-life, and use decay constants to solve problems involving nuclear instability.

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    Radioactive decay (A-level only) explained

    Radioactive decay has practical consequences because each nuclide has a characteristic half-life and type of emission.

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    In waste storage, long half-life nuclides such as plutonium-239 remain hazardous for thousands of years, so they are vitrified in glass, sealed in steel canisters and buried deep underground to isolate them while activity falls. Short half-life waste can be stored until its activity is negligible. In radioactive dating, the ratio of parent to daughter nuclei is measured. For carbon-14 dating, living material exchanges carbon until death; afterwards carbon-14 decays with a half-life of about 5730 years, so the remaining fraction gives an age up to roughly 50000 years. For rocks, uranium-lead dating uses a very long half-life, so it works over billions of years. The same decay equations and half-life calculations underpin both applications.

    Read the Radioactive decay (A-level only) study guideFull revision notes for AQA A-Level Physics

    Your focus

    1. Explain how half-life and radiation type determine a suitable method for storing radioactive waste.
    2. Use parent-to-daughter ratios and half-life data to calculate the age of a sample.
    3. Compare the suitability of different radioisotopes for dating over different time ranges.

    Which command word is this?

    Give a precise, formal statement that matches the mark scheme exactly. For half-life, you must mention 'time for number of undecayed nuclei (or activity) to halve'. No examples or extra detail needed.

    Radioactive decay (A-level only) exam tips

    Topic Overview

    Radioactive decay is a fundamental topic in AQA A-Level Physics that explores the spontaneous and random disintegration of unstable atomic nuclei. You will study the three main types of radiation (alpha, beta and gamma), their properties, and how they interact with matter and magnetic fields. The topic also introduces the exponential decay law, activity, decay constant and half-life, which are essential for understanding nuclear stability and dating techniques.

    This topic matters because it underpins many real-world applications, from medical imaging and cancer treatment to carbon dating and nuclear power. It also develops your ability to handle exponential functions and logarithms in a physical context, skills that are examined in both written papers and practical assessments. A strong grasp of radioactive decay is crucial for later topics such as nuclear energy and particle physics.

    Key Concepts
    • →Radioactive decay is spontaneous and random: it is unaffected by external conditions and you cannot predict which nucleus decays or when.
    • →Alpha decay emits a helium nucleus (2 protons, 2 neutrons), beta-minus decay emits an electron and an antineutrino, and gamma decay emits a high-energy photon. Each changes the nucleus in different ways.
    • →Activity (A) is the rate of decay, measured in becquerels (Bq), where 1 Bq = 1 decay per second. It decreases exponentially over time.
    • →The decay constant (lambda) is the probability of decay per nucleus per second, with units s^-1. It is related to half-life by t_half = ln(2) / lambda.
    • →The exponential decay equation A = A0 e^(-lambda t) (or N = N0 e^(-lambda t)) describes how activity or number of undecayed nuclei changes with time.
    Marking Points
    • State that the hazard of radioactive waste depends on half-life, activity and type of radiation emitted.
    • Explain that long half-life waste remains radioactive for a very long time, so isolation from the environment is needed.
    • Describe storage methods such as vitrification, sealing in canisters and deep geological disposal.
    • Explain that short half-life waste can be stored until its activity has fallen to a safe level.
    • Describe radioactive dating as using the ratio of parent to daughter nuclei and the known half-life.
    • Apply the decay equation or half-life relationship to calculate an age or a remaining fraction.
    • Compare carbon-14 dating with uranium-lead dating in terms of useful range and half-life.
    Examiner Tips
    • 💡Link each application to the half-life value and the type of radiation emitted, not just to the word radioactive.
    • 💡Show the decay calculation clearly, including the fraction remaining and the number of half-lives.
    • 💡Use precise terms such as parent nuclei, daughter nuclei, activity, half-life and isolation when describing waste storage.
    • 💡Always define half-life in terms of 'number of undecayed nuclei' or 'activity', not 'mass' or 'count rate', unless the question specifically asks for count rate.
    • 💡When using the exponential decay equation, ensure all units are consistent (time in seconds, activity in Bq) and show your rearrangement clearly to gain method marks.
    • 💡For 'explain' questions on randomness, use the precise wording: 'spontaneous' means not affected by external factors, and 'random' means you cannot predict which nucleus decays or when.
    Common Mistakes
    • Thinking that a long half-life means the waste is safe because activity is low; correction: a long half-life means it stays radioactive for a very long time, so isolation is needed for thousands of years.
    • Confusing half-life with the time for all activity to stop; correction: activity halves in each half-life and never reaches exactly zero in a finite time.
    • Using carbon-14 dating for samples older than about 50000 years or for non-living material; correction: carbon-14 has a relatively short half-life and only dates once-living material over a limited range.
    • Students often think that after one half-life, all the radioactive material has gone. In fact, half of the undecayed nuclei remain, and the activity halves, but the sample never reaches zero activity in theory.
    • Many believe that heating or applying pressure can speed up radioactive decay. Radioactive decay is spontaneous and unaffected by external factors such as temperature, pressure or chemical state.
    • Some confuse the penetrating power of radiation: alpha is the least penetrating (stopped by paper), beta is stopped by a few mm of aluminium, and gamma is the most penetrating (requires thick lead). Remember that alpha is the most ionising, not the least.
    Revision Plan
    1. 1Day 1-2: Review the three types of radiation (alpha, beta, gamma) and their properties, including penetration, ionisation and behaviour in electric/magnetic fields. Make a comparison table.
    2. 2Day 3-4: Learn the definitions of activity, decay constant and half-life. Practice converting between units (Bq, kBq, MBq) and using t_half = ln(2) / lambda.
    3. 3Day 5-6: Master the exponential decay equation A = A0 e^(-lambda t) and N = N0 e^(-lambda t). Solve problems involving finding activity, time, or decay constant, ensuring unit consistency.
    4. 4Day 7-8: Work through exam-style questions, especially those requiring explanations of randomness and spontaneity. Mark your answers against the mark scheme and note key phrases.
    5. 5Day 9-10: Create flashcards for key definitions and formulas. Test yourself on active recall prompts and past paper questions under timed conditions.
    Exam Question Types
    • 📋Definition and explanation questions: e.g. 'Define half-life' or 'Explain why radioactive decay is random and spontaneous.' Use precise terminology and avoid vague language.
    • 📋Calculation questions: e.g. 'Calculate the activity after a given time' or 'Determine the half-life from a graph of activity against time.' Show all steps and units.
    • 📋Graph analysis: e.g. 'Sketch a graph of activity against time and explain its shape.' Remember it is an exponential decay curve, never touching the time axis.
    • 📋Practical application: e.g. 'Describe an experiment to determine the half-life of a radioactive source.' Include details of background radiation correction and repeated readings.
    Command Word Expectations (AQA)
    Define

    Give a precise, formal statement that matches the mark scheme exactly. For half-life, you must mention 'time for number of undecayed nuclei (or activity) to halve'. No examples or extra detail needed.

    Explain

    Provide a reasoned account that links cause and effect. For randomness, you must state that it is impossible to predict which nucleus decays or when, and that it is spontaneous (unaffected by external factors). Use the word 'because' to connect points.

    Calculate

    Show your working, including the equation used, substitution of values with units, and the final answer with correct units and significant figures. Method marks are awarded for correct rearrangement and substitution even if the final answer is wrong.

    How Students Lose Marks (Examiner Pitfalls)
    Pitfall: Students often state that half-life is 'the time for half the atoms to decay' without specifying that it is the time for the number of undecayed nuclei (or activity) to halve. They also fail to recognise that radioactive decay is a random process, meaning you cannot predict which nucleus decays next or when a specific nucleus will decay.
    ❌ Weak Answer (Loses Marks):Half-life is how long it takes for half of the radioactive material to disappear. It is random so you cannot know when it will decay.
    Example improved answer:Half-life is the average time taken for the number of undecayed nuclei in a sample to halve, or for the activity of a source to halve. Radioactive decay is a spontaneous and random process: spontaneous means it is not affected by external factors such as temperature or pressure, and random means it is impossible to predict which nucleus will decay next or when a particular nucleus will decay.
    Examiner Tip: Always use the precise phrase 'number of undecayed nuclei' or 'activity' when defining half-life. When explaining randomness, mention both 'which nucleus' and 'when' to secure all marks.
    Pitfall: In calculations, students frequently forget to convert units (e.g. kBq to Bq, days to seconds) or misapply the exponential decay equation by using the wrong power or confusing lambda with half-life. They also lose marks by not showing the rearrangement of the equation or by rounding too early.
    ❌ Weak Answer (Loses Marks):A = A0 e^(-lambda t). I put the numbers in and got an answer but forgot to convert kBq to Bq so my final answer was wrong by a factor of 1000.
    Example improved answer:First convert all units: activity in Bq, time in seconds, decay constant in s^-1. Use the equation A = A0 e^(-lambda t). Rearrange to find lambda if needed: lambda = ln(2) / t_half. Substitute values carefully, keep full precision until the final answer, then round to an appropriate number of significant figures (usually 2 or 3). State the unit (Bq) with your final answer.
    Examiner Tip: Always write down the equation, substitute numbers with units, and show intermediate values. Check that your answer is sensible: activity should decrease with time, and half-life should be positive.
    Step-by-Step Worked Solutions

    Question: A radioactive source has an initial activity of 8000 Bq and a half-life of 12 days. Calculate the activity after 36 days.

    1. 1.Step 1: Identify given facts: A0 = 8000 Bq, t_half = 12 days, t = 36 days. Note that 36 days is exactly 3 half-lives (36 / 12 = 3).
    2. 2.Step 2: Apply the half-life relationship: after n half-lives, A = A0 / (2^n). Here n = 3, so A = 8000 / (2^3) = 8000 / 8.
    3. 3.Step 3: Calculate final activity: A = 1000 Bq. State the unit clearly.
    Final Answer: The activity after 36 days is 1000 Bq.

    Question: A sample of radioactive isotope has a decay constant of 0.025 s^-1. Calculate the half-life of the isotope and the time taken for the activity to fall to 20% of its initial value.

    1. 1.Step 1: Use the relationship between half-life and decay constant: t_half = ln(2) / lambda. Substitute lambda = 0.025 s^-1: t_half = 0.693 / 0.025 = 27.7 s (to 3 s.f.).
    2. 2.Step 2: For the activity to fall to 20% of its initial value, A = 0.20 A0. Use A = A0 e^(-lambda t). Rearrange: 0.20 = e^(-0.025 t). Take natural logs: ln(0.20) = -0.025 t.
    3. 3.Step 3: Solve for t: t = ln(0.20) / -0.025 = (-1.609) / -0.025 = 64.4 s (to 3 s.f.). State units.
    Final Answer: Half-life = 27.7 s; time to fall to 20% activity = 64.4 s.
    Active Recall Memory Test
    What is the definition of half-life?
    Key Fact: Half-life is the average time taken for the number of undecayed nuclei in a sample to halve, or for the activity of a source to halve.
    State the relationship between half-life and the decay constant.
    Key Fact: t_half = ln(2) / lambda, where lambda is the decay constant in s^-1.
    What is meant by the statement 'radioactive decay is random'?
    Key Fact: It means it is impossible to predict which nucleus will decay next or when a particular nucleus will decay.
    Write the exponential decay equation for activity.
    Key Fact: A = A0 e^(-lambda t), where A is activity at time t, A0 is initial activity, lambda is decay constant, and t is time.
    Frequently Asked Questions
    What is the difference between alpha, beta and gamma radiation?
    Alpha radiation is a helium nucleus (2 protons, 2 neutrons) with a charge of +2e. It is highly ionising but poorly penetrating, stopped by paper or a few cm of air. Beta-minus radiation is a fast-moving electron (charge -1e) emitted when a neutron converts to a proton; it is moderately ionising and penetrating, stopped by a few mm of aluminium. Gamma radiation is a high-energy photon with no charge or mass; it is weakly ionising but highly penetrating, requiring thick lead or concrete to reduce it significantly.
    How do you calculate the half-life from a graph of activity against time?
    Plot activity on the y-axis and time on the x-axis. Identify the initial activity, then find the time at which the activity has fallen to half of that initial value. That time is the half-life. You can repeat this for several half-lives and take an average to improve accuracy. The graph should be an exponential decay curve, so it never touches the time axis.
    Why is radioactive decay described as spontaneous?
    Spontaneous means that the decay is not caused or influenced by external factors such as temperature, pressure, chemical state, or the presence of other nuclei. It happens naturally and randomly, without any external trigger. This is a fundamental property of unstable nuclei.
    What is the decay constant and what are its units?
    The decay constant (lambda) is the probability that an individual nucleus will decay per unit time. It is a constant for a given isotope and is related to half-life by t_half = ln(2) / lambda. Its units are per second (s^-1), because it represents a probability per unit time.
    Can the activity of a radioactive source ever reach zero?
    In theory, the activity decreases exponentially and never quite reaches zero, because the number of undecayed nuclei approaches zero asymptotically. In practice, after many half-lives, the activity becomes so low that it is indistinguishable from background radiation, and the source is considered effectively inactive. However, mathematically, it never reaches exactly zero.
    How do you correct for background radiation in half-life experiments?
    Measure the background count rate with no source present, using the same detector and for the same duration. Then subtract this background count rate from each measured count rate with the source present. This gives the corrected count rate due to the source alone. Always correct before calculating ratios or plotting graphs, as background radiation can significantly affect results, especially when the source activity is low.