Radioactivity — OCR A-Level Physics

This guided reading covers the techniques and procedures used to investigate the absorption of alpha particles, beta particles and gamma rays by appropriate materials. You will learn how to set up a source, absorber and detector to measure radiation intensity, and how to analyse the results to compare penetration and range. The aim is to understand how different materials absorb different types of radiation, and to be able to describe a safe and accurate experiment. You should focus on the choice of absorber material and thickness, the use of a Geiger-Müller tube and counter, and the need to correct for background radiation. You will also consider how to vary the thickness systematically and plot a graph of count rate against thickness to determine absorption characteristics.

Alpha particles are helium nuclei (2 protons and 2 neutrons), with charge 2⁺ and mass number 4. They are highly ionising but have low penetration, stopped by paper or a few centimetres of air. Beta particles are fast-moving electrons (or positrons), with charge 1⁻ or 1⁺ and negligible mass; they are less ionising than alpha but more penetrating, stopped by a few millimetres of aluminium. Gamma rays are high-energy electromagnetic radiation, with no charge or mass; they are the least ionising and most penetrating, requiring several centimetres of lead to reduce intensity. Range in air: alpha a few centimetres, beta a few metres, gamma effectively unlimited but attenuated. Penetration depends on ionising power and interactions with matter.

To investigate absorption, set up a source, absorber and detector (e.g., Geiger-Müller tube) with a counter. Measure background count rate first and subtract it from all readings. For alpha, use paper or thin card as absorber; for beta, use aluminium sheets of varying thickness; for gamma, use lead sheets. Vary absorber thickness systematically and record count rate. Plot corrected count rate against thickness. Alpha shows a sharp cut-off (definite range); beta and gamma show exponential decrease. Use tongs to handle sources, minimise exposure time, and keep source away from body. Ensure distance between source and detector is constant. This experiment allows comparison of penetration and absorption characteristics.

Nuclear decay equations track changes in proton and nucleon numbers. Alpha emission removes a helium nucleus, so the parent loses two protons and two neutrons: for example, ²³⁸U → ²³⁴Th + ⁴He. Beta-minus decay converts a neutron into a proton and emits an electron and an antineutrino: ¹⁴C → ¹⁴N + ⁰e + antineutrino. Beta-plus decay converts a proton into a neutron and emits a positron and a neutrino: ²²Na → ²²Ne + ⁰e + neutrino. Balancing means the total nucleon number and total proton number are equal on both sides. Use the nuclide notation with mass number as a superscript and atomic number as a subscript, and include the emitted particle with its own numbers.

Activity A is the number of nuclear decays per second, measured in becquerels (Bq). The decay constant λ (often written as m in some texts) is the probability of decay per nucleus per unit time, with unit s⁻¹. For a sample containing N undecayed nuclei, activity is given by A = λN. This means a larger decay constant or more nuclei gives a higher activity. For example, if a source has N = 2.0 × 10²⁰ nuclei and λ = 1.0 × 10⁻⁶ s⁻¹, then A = 2.0 × 10¹⁴ Bq. Activity decreases over time as N falls, so A is not constant. The equation applies to any radionuclide and is fundamental to radioactive decay calculations.

This guided reading note supports study of the OCR A Level Physics A specification section 6.4.3 Radioactivity. The statement is incomplete, so you should use the official specification to identify the full learning point. Read the relevant pages of your textbook or revision guide, and make notes on definitions, equations and graphs. For example, if the statement covers half-life, note the definition and the equation λt₁/₂ = ln 2. Check that you can explain each term and apply it to calculations. Use the specification to confirm what is required, and practise interpreting decay curves and solving numerical problems. This approach builds accurate understanding for assessment.

Half-life t₁/₂ is the average time taken for half the nuclei in a sample to decay, or for the activity to halve. It is a constant for a given isotope. The decay constant λ (sometimes written m) is related to half-life by λ t₁/₂ = ln 2, where ln 2 ≈ 0.693. This equation allows conversion between λ and t₁/₂. For example, if t₁/₂ = 5.0 years, then λ = ln 2 / 5.0 ≈ 0.139 year⁻¹. Half-life can range from fractions of a second to billions of years. In calculations, ensure time units are consistent. The equation is used in problems involving activity, number of nuclei and decay constant.

This row is a numbering label, not a teachable statement. It marks the second item within a numbered list in section 6.4.3 Radioactivity, so it tells you where you are in the specification sequence rather than what physics to learn. Read it as a signpost: the content you must actually study sits in the neighbouring rows, such as the decay equations, the half-life definition and the experimental techniques for measuring half-life. When revising, use the numbered items around it to build a checklist, and treat this label only as an index entry. Do not invent a definition, equation or practical skill from the number itself, and do not quote it as an assessed objective.

Half-life is the time for the number of undecayed nuclei, or the activity, to fall to half its initial value. To determine it experimentally, a source such as protactinium-234 is used because it has a conveniently short half-life. A sample is placed near a Geiger-Muller tube connected to a counter or ratemeter, and the count rate is recorded at regular time intervals. Background count rate is measured with the source removed and subtracted from each reading. Corrected count rate is plotted against time on a graph, and the half-life is read as the time for the count rate to halve, or found from a suitable exponential fit. Repeating readings and using consistent geometry reduce random and systematic error.

This row is a lettered label, not a teachable statement. It marks a sub-section heading within 6.4.3 Radioactivity, so it functions as a signpost in the specification rather than as physics content. Read it as an instruction to look at the items grouped under it, which include the decay equations and the practical techniques for measuring half-life. When revising, use the lettered structure to organise your notes and to check that every substantive clause in the group has been covered. Do not attempt to define the letter itself, and do not treat it as an assessed objective or a mark-bearing statement.

These equations describe exponential decay of activity and of undecayed nuclei. In the intended form, A = A₀e^(−λt) and N = N₀e^(−λt), where A is activity at time t, A₀ is initial activity, N is the number of undecayed nuclei at time t, N₀ is the initial number, λ is the decay constant and t is elapsed time. Activity is the rate of decay, measured in becquerels, where 1 Bq = 1 decay per second. The decay constant λ has unit s⁻¹. Because both A and N follow the same exponential form, the ratio A/N is constant and equals λ. Half-life is related to the decay constant by T½ = ln2/λ. The equations apply to large numbers of nuclei and describe random decay statistically.

Radioactive decay is random and spontaneous, so a single nucleus's fate cannot be predicted, yet large samples show exponential decay. A dice simulation models this: each die represents a nucleus, and a chosen face (say a 6) means that nucleus has decayed. Roll all dice, remove those showing 6, and record the number remaining after each throw. The fraction surviving per throw is 5/6, so the count falls by a constant factor each round, producing an exponential curve. With many dice the decay is smooth; with few, random fluctuation is visible. This links the probabilistic nature of decay to the decay constant λ and the equation N = N₀e^(−λt).

This statement requires using graphical methods and iterative spreadsheet modelling for the radioactive decay rate equation $\Delta N/\Delta t = -\lambda N$. Rather than using the analytic exponential solution, spreadsheet modelling involves a step-by-step numerical method. Starting with an initial number of undecayed nuclei $N_0$ and a chosen time interval $\Delta t$, the change in nuclei is calculated as $\Delta N = -\lambda N \Delta t$. The new number of nuclei after $\Delta t$ is then $N_{new} = N_{old} + \Delta N$. This process is repeated iteratively across rows in a spreadsheet to generate a decay curve. For the model to be accurate, the time interval $\Delta t$ must be significantly smaller than the half-life. Graphical methods involve plotting the modelled values of $N$ against $t$ to visualise the exponential decay curve and determine the half-life.

Radioactive dating uses the known decay of a radionuclide to estimate the age of a material. In carbon dating, living things exchange carbon with the atmosphere, so the proportion of carbon-14 remains roughly constant while they are alive. When they die, exchange stops and the carbon-14 decays with a half-life of about 5730 years. Measuring the remaining carbon-14 activity or ratio allows the age to be estimated using N = N₀e^(−λt) or the half-life relationship. The method is limited to materials that were once living and to ages up to roughly 50 000 years, because beyond that too little carbon-14 remains to measure reliably.