Rutherford scattering (A-level only) — AQA A-Level Physics

Rutherford scattering is the experimental evidence that led to the nuclear model of the atom. In 1909, Geiger and Marsden, working under Rutherford, fired alpha particles at a very thin gold foil and observed the angles through which the particles were scattered. The results were completely unexpected: most alpha particles passed straight through, but a small number were deflected through angles greater than 90 degrees. This could not be explained by the prevailing plum pudding model, which assumed positive charge was spread evenly throughout the atom.

The experiment is A-level only because it requires quantitative analysis using Coulomb's law and conservation of energy. You need to be able to explain the observations in terms of the electrostatic force between the alpha particle and the nucleus, and to calculate the distance of closest approach, which gives an upper limit for the nuclear radius. This topic also introduces the idea that the nucleus is tiny compared to the atom and contains most of the atom's mass, which is fundamental to understanding atomic structure and later topics such as nuclear physics and particle physics.

• →The atom is mostly empty space with a very small, dense, positively charged nucleus at the centre. The nucleus contains almost all the mass of the atom.
• →Alpha particles are helium nuclei (2 protons and 2 neutrons) with a charge of +2e. They experience an electrostatic repulsive force when close to a nucleus, described by Coulomb's law: F = kQq/r^2.
• →Most alpha particles pass straight through the foil because they do not come close enough to a nucleus for the repulsive force to cause significant deflection. A few are deflected through large angles because they pass very close to a nucleus, where the repulsive force is strong.
• →The distance of closest approach is the minimum distance between an alpha particle and a nucleus when the alpha particle is back-scattered through 180 degrees. At this point, all kinetic energy is converted to electric potential energy: kQq/r = E_k.
• →The distance of closest approach gives an upper limit for the radius of the nucleus because the alpha particle is repelled before it can touch the nucleus. The actual nuclear radius is smaller than this value.

• Most alpha particles pass through the foil with little or no deflection, so most of the atom is empty space.
• A small proportion are deflected through large angles, so the atom contains a concentrated region of positive charge.
• Very few are deflected back towards the source, so this positive region is extremely small and dense.
• The deflection is caused by electrostatic repulsion between the positive alpha particle and the positive nucleus.
• The closer the alpha particle passes to a nucleus, the greater the repulsive force and the larger the deflection.
• The plum-pudding model cannot explain large-angle or backward scattering because its positive charge is spread thinly throughout the atom.
• Thomson's plum-pudding model described positive charge spread throughout the atom with electrons embedded in it.
• Rutherford's alpha-scattering evidence showed a tiny, dense, positively charged nucleus, replacing the plum-pudding model.
• The discovery of the proton and the neutron established that the nucleus contains both types of nucleon.
• Deep inelastic scattering experiments provided evidence that protons and neutrons contain quarks.
• Each change followed new experimental evidence that the previous model could not explain.
• Scientific models are provisional and are refined or replaced as evidence and techniques improve.
• Alpha particles are helium nuclei with charge 2⁺ and are strongly ionising but have a short range in air, so they are stopped by paper or skin.
• Beta particles are fast electrons with charge 1⁻; they are less ionising than alpha but more penetrating, and are absorbed by a few millimetres of aluminium.
• Gamma radiation is electromagnetic radiation with no charge and no mass; it is weakly ionising but highly penetrating, so thick lead or concrete reduces its intensity.
• In an absorption experiment, count rate is measured with and without the absorber, background count is subtracted, and the change identifies the radiation type.
• Relative hazard depends on penetration and ionisation: external alpha is largely stopped by dead skin, but inhaled or ingested alpha emitters are serious internal hazards; gamma is an external hazard because it reaches internal organs.
• Practical safety measures include minimising exposure time, increasing distance and using appropriate shielding.
• A radioactive source and detector are placed on opposite sides of the moving sheet, and the count rate indicates the thickness of material between them.
• Beta radiation is suitable for measuring thin materials such as paper and aluminium foil because beta is partly absorbed by small thicknesses.
• Gamma radiation is suitable for measuring thicker or denser materials such as steel because gamma is highly penetrating and is not completely stopped by thin sheets.
• A fall in count rate indicates increased thickness, while a rise indicates reduced thickness, because more material absorbs more radiation.
• The count rate is compared with a reference value and a feedback system adjusts the rollers to maintain the required thickness.
• The method is non-contact and can operate continuously on a moving production line.
• Alpha particles are highly ionising but have a short range in air, so external exposure is low risk while internal exposure is serious.
• Beta particles require a few millimetres of a low-Z absorber such as aluminium or Perspex, as high-Z absorbers like lead produce more bremsstrahlung.
• Gamma rays are penetrating and need dense, thick shielding such as lead or concrete to attenuate them.
• Safe handling reduces dose by minimising time, maximising distance and using appropriate shielding.
• Sealed sources should be handled with tongs, stored in labelled containers and never pointed towards people.
• Dose monitoring with a film badge or Geiger–Müller tube provides evidence that exposure is being controlled.
• Background radiation is ionising radiation present in the environment when no source is deliberately introduced.
• Origins include radon gas, cosmic rays, naturally occurring radioisotopes such as potassium-40, and artificial sources such as medical or industrial use.
• A detector records background counts in addition to counts from the source, so raw readings overestimate source activity.
• The background count rate is measured with the source removed, ideally over the same counting time and repeated to average random fluctuations.
• Corrected count rate equals measured count rate minus background count rate, with units retained.
• Subtracting background improves the accuracy of half-life or absorption measurements by removing a constant offset.
• Identifies the benefit of a named medical use, such as diagnosis of disease or destruction of tumour tissue.
• Identifies the risk, such as ionising damage to DNA, cell mutation or induced cancer.
• Compares risk and benefit for the specific patient group and procedure rather than in general terms.
• Uses physics ideas such as absorbed dose, equivalent dose, half-life, penetrating power or source type to support the comparison.
• Recognises that benefit may justify higher risk in therapy than in diagnosis, and that alternatives and patient factors matter.
• Measures background count rate with the source removed or shielded and subtracts it from each reading.
• Records distance from the source to a fixed reference point on the detector, keeping the detector and source aligned.
• Plots corrected count rate against 1/d² and interprets a straight line through the origin as evidence for the inverse-square law.
• Controls variables such as source activity, detector settings and measurement time, and repeats readings to reduce random uncertainty.
• Uses safe handling: tongs, minimum time, maximum distance, shielding and secure storage of the source.

• 💡Link each observation to a conclusion about atomic structure rather than describing the apparatus alone.
• 💡Use the phrase 'electrostatic repulsion' when explaining why an alpha particle changes direction.
• 💡When comparing with the plum-pudding model, state explicitly which observation it cannot explain.
• 💡Sequence the models in time and name the key evidence that prompted each change.
• 💡Use words such as 'evidence', 'model' and 'replaced' to show how understanding developed.
• 💡Avoid implying that the current model is final; describe it as the best explanation of current evidence.
• 💡When describing an absorption test, state the absorber used, the measurement taken and the conclusion drawn for each radiation type.
• 💡Link hazard to the route of exposure: external exposure, inhalation or ingestion changes which radiation is most dangerous.
• 💡Use comparative language such as more ionising, less penetrating and stopped by, rather than absolute statements.
• 💡Name the radiation and the material together, for example beta for paper and gamma for steel, and justify the choice by penetration.
• 💡Describe the sequence: source, material, detector, count rate, comparison, adjustment.
• 💡State the relationship between thickness and count rate clearly, using falls and rises correctly.
• 💡Name the radiation type and match it to a specific absorber with a reason, rather than writing 'lead stops radiation' for every case.
• 💡Use the time–distance–shielding framework to structure safety answers and apply each factor to the source in the question.
• 💡Remember that low-Z materials are preferred for shielding beta sources to minimise the production of penetrating bremsstrahlung X-rays.
• 💡State clearly that background is measured with the source removed, then show the subtraction explicitly in your working.
• 💡Keep units consistent, for example counts per minute minus counts per minute, and quote the corrected value with its unit.
• 💡When describing improvements, mention repeating the background count and averaging to reduce the effect of random fluctuations.
• 💡Name the procedure and the radionuclide or radiation type before discussing risk and benefit.
• 💡Use comparative language such as greater than, lower than or justified because to show balance.
• 💡Link each risk or benefit to a physics quantity, such as dose in sieverts or half-life in hours, rather than asserting it.
• 💡State the background correction explicitly and show one worked subtraction.
• 💡Use a log or ratio check, such as doubling distance should quarter the corrected count rate, to test the law.
• 💡Comment on why very small distances may not fit the inverse-square law, referring to source and detector size.
• 💡When explaining the Rutherford scattering results, always link each observation to a conclusion about the structure of the atom. For example: 'Most alpha particles pass straight through, which shows the atom is mostly empty space.' This is a common 2-mark question.
• 💡In calculations, always convert kinetic energy from MeV to joules before using the equation kQq/r = E_k. Show your working clearly, including the charges on the alpha particle (+2e) and the nucleus (+Ze). State that the answer is an upper limit for the nuclear radius.
• 💡Use precise terminology: 'electrostatic repulsion', 'Coulomb's law', 'distance of closest approach', 'upper limit'. Avoid vague words like 'bounce' or 'hit'. If asked to explain why the nucleus is small, refer to the fact that only a tiny fraction of alpha particles are deflected through large angles.

• Saying alpha particles are attracted to the nucleus: the error is ignoring that both alpha particle and nucleus are positive, so the force is repulsive.
• Claiming most alpha particles are deflected: the error is reversing the observed pattern; most pass through nearly undeflected.
• Stating that the nucleus is the same size as the atom: the error is ignoring that backward scattering requires a very small, dense nucleus.
• Presenting the plum-pudding model as simply wrong from the start: the error is ignoring that it was a reasonable model for the evidence then available.
• Saying Rutherford discovered the electron: the error is confusing Rutherford's nuclear model with Thomson's earlier identification of the electron.
• Claiming the nucleus has always been understood as protons and neutrons: the error is ignoring the later discovery of the neutron and of quarks.
• Treating beta as more ionising than alpha: alpha is the most ionising because it is heavily charged and slow-moving, while beta is less ionising.
• Forgetting to subtract background count: the corrected count rate is the measured rate minus the background rate, otherwise absorption conclusions are unreliable.
• Assuming all gamma is stopped by a thin aluminium sheet: aluminium absorbs beta, but gamma requires much thicker, denser shielding such as lead.
• Choosing alpha for thickness measurement: alpha is stopped by air and by very thin layers, so it cannot penetrate the sheet reliably.
• Saying that a higher count rate means a thicker sheet: greater thickness absorbs more radiation, so the count rate falls.
• Ignoring background count: background must be subtracted before comparing the measured count rate with the reference value.
• Thinking that any absorber stops all radiation: correction is that alpha is stopped by paper, beta by a few millimetres of aluminium, and gamma is only attenuated by thick lead or concrete.
• Believing distance does not matter because shielding is present: correction is that intensity falls with distance, so tongs and remote handling reduce dose further.
• Treating an alpha source as harmless because its range is short: correction is that inhaled or swallowed alpha emitters deliver concentrated dose to living tissue and must be kept sealed.
• Forgetting to subtract background and reporting the raw count rate as the source count rate: correction is to measure background with the source removed and subtract it from every reading.
• Subtracting background only once from a total rather than from each individual reading: correction is to subtract the background count rate from each measured count rate before plotting or averaging.
• Assuming background is negligible because it is small: correction is that background can be a large fraction of a weak source's count rate and must still be measured and subtracted.
• Treating radiation as either wholly safe or wholly harmful; the correction is to weigh the specific benefit against the specific risk for that procedure.
• Confusing the risk to the patient with the risk to the radiographer; the correction is to state which person receives which dose and why shielding, distance and time reduce staff dose.
• Assuming all medical radiation is gamma; the correction is to match the radiation type to the use, for example beta emitters for therapy and gamma emitters for imaging.
• Forgetting to subtract background count rate; the correction is to measure background separately and subtract it from every reading before plotting.
• Measuring distance from the source to the bench end rather than to the detector; the correction is to define and use a consistent source-to-detector distance.
• Plotting count rate against distance and expecting a straight line; the correction is to plot against 1/d² or to check that count rate falls by a factor of four when distance doubles.
• Students often say that alpha particles 'bounce off' or 'hit' the nucleus. This is incorrect because the alpha particle never touches the nucleus; it is repelled by the electrostatic force and reverses direction before contact. Always refer to 'electrostatic repulsion' and 'distance of closest approach'.
• Students sometimes think that the large-angle deflections are due to collisions with electrons. This is wrong because electrons are much less massive than alpha particles and cannot cause large deflections. The deflections are due to the positively charged nucleus.
• Students may forget that the distance of closest approach is an upper limit for the nuclear radius, not the actual radius. The alpha particle is repelled before it reaches the nucleus, so the nucleus must be smaller than the calculated distance.

1. 1Day 1: Watch a video or read a textbook section on the Rutherford scattering experiment. Make a timeline of the experiment and note the key observations and conclusions. Write a summary in your own words.
2. 2Day 2: Learn the quantitative analysis. Derive the equation for distance of closest approach from conservation of energy. Practice converting MeV to J and substituting values for alpha particles and gold nuclei.
3. 3Day 3: Work through exam-style questions on Rutherford scattering. Focus on 6-mark explanation questions and calculation questions. Check your answers against mark schemes and note where you lose marks.
4. 4Day 4: Create a set of flashcards for the key concepts, equations, and common misconceptions. Test yourself on the active recall prompts. Review any topics you find difficult.
5. 5Day 5: Complete a past paper question on this topic under timed conditions. Mark it strictly and review your mistakes. Revisit any areas of weakness before moving on.

• 📋Explanation questions (4-6 marks): Describe the Rutherford scattering experiment and explain how the results led to the nuclear model. Advice: Structure your answer around the observations (most undeflected, few large-angle deflections) and link each to a conclusion about the atom.
• 📋Calculation questions (3-4 marks): Calculate the distance of closest approach given the kinetic energy of the alpha particle and the atomic number of the foil. Advice: Convert MeV to J, use kQq/r = E_k, and state that the answer is an upper limit for the nuclear radius.
• 📋Graph or data analysis questions (2-3 marks): Interpret a graph of number of alpha particles scattered against angle of scattering. Advice: Describe the shape (most at small angles, few at large angles) and explain it in terms of the probability of close approach to a nucleus.
• 📋Practical questions (2-3 marks): Explain why the experiment is performed in a vacuum and why a very thin foil is used. Advice: Vacuum prevents alpha particles from colliding with air molecules; thin foil ensures only single scattering events occur.