Nuclear Physics

• The chapter in one sentence: a tiny, massive, positively charged nucleus can be unstable; when it is, it changes spontaneously and at random, emitting alpha, beta or gamma radiation whose different ionising and penetrating properties decide how we detect it, what we use it for and how we stay safe near it.
• Six-word audit for any Topic 5 answer: which particle, which property, which number? Name the particle or emission, name the property you are using (ionising, penetrating, charge, mass, half-life), and quote the number you changed (\(A\), \(Z\), corrected count rate, time).
• Exam-safe answer model for 5.2.3: "Alpha: \(A\) down \(4\), \(Z\) down \(2\). Beta: \(A\) same, \(Z\) up \(1\). Gamma: both the same. Balance the top row and the bottom row separately, and remember the beta particle's bottom number is \(-1\)." Mastery check: can you complete any of the three equation types and verify it with both sums?
• Before you write a single Topic 5 sentence, ask three things: which particle or emission am I talking about; which property am I using (ionising, penetrating, charge, mass, half-life); and which number changed (\(A\), \(Z\), corrected count rate, time)? An answer that names all three is almost always creditable. An answer that names none of them almost never is.
• The final gate. Cover this page and write, from memory: the three scattering conclusions; \(N = A - Z\); the two reversed ranking orders; the three decay rules for \(A\) and \(Z\); the three reactor verbs; the definition of half-life; and the three safety factors. If all seven come out clean, Topic 5 is done.

• 5.1.1 — Describe the structure of the atom as a positively charged nucleus with negatively charged electrons in orbit around it.
• 5.1.1 — Describe how alpha-particle scattering experiments give evidence for a very small nucleus surrounded by mostly empty space, for a nucleus containing most of the mass of the atom, and for a nucleus that is positively charged.
• 5.1.2 — Describe the composition of the nucleus in terms of protons and neutrons.
• 5.1.2 — Describe how atoms form positive ions by losing electrons and negative ions by gaining electrons.
• 5.1.2 — Define proton number (atomic number) \(Z\) and nucleon number (mass number) \(A\), and calculate the number of neutrons in a nucleus.
• 5.1.2 — Explain the term nuclide and use nuclide notation \({}^{A}_{Z}\mathrm{X}\).
• 5.1.2 — Explain what is meant by an isotope, and state that an element may have more than one isotope.
• 5.2.1 — Describe the detection of alpha particles using a cloud chamber or a spark counter, and the detection of beta particles and gamma radiation using a Geiger–Müller tube and counter.
• 5.2.1 — Use count rate measured in counts/s or counts/minute.
• 5.2.1 — State what is meant by background radiation.
• 5.2.1 — Name the sources that make a significant contribution to background radiation: radon gas in the air, rocks and buildings, food and drink, and cosmic rays.
• 5.2.1 — Use a measurement of background radiation to determine a corrected count rate.
• 5.2.2 — Describe the emission of radiation from a nucleus as spontaneous and random in direction.
• 5.2.2 — Describe alpha particles as two protons and two neutrons (helium nuclei), beta particles as high-speed electrons from the nucleus, and gamma radiation as high-frequency electromagnetic waves.
• 5.2.2 — State the relative ionising effects and the relative penetrating powers of alpha particles, beta particles and gamma radiation.
• 5.2.2 — Describe the deflection of alpha particles, beta particles and gamma radiation in electric fields and in magnetic fields.
• 5.2.3 — State that radioactive decay is a change in an unstable nucleus that can emit alpha or beta particles and/or gamma radiation, and that these changes are spontaneous and random.
• 5.2.3 — Use decay equations in nuclide notation to show alpha emission, beta emission and gamma emission.
• 5.2.4 — Describe fusion as the formation of a larger nucleus by combining two smaller nuclei with the release of energy, and recognise fusion as the energy source for stars.
• 5.2.4 — Describe fission as a nucleus such as uranium-235 absorbing a neutron and producing daughter nuclei and two or more neutrons with the release of energy.
• 5.2.4 — Explain how the neutrons produced in fission create a chain reaction, and how that reaction is controlled in a nuclear reactor by the coolant, the moderator and the control rods.
• 5.2.5 — Define the half-life of a particular isotope and use the definition in calculations, including calculations based on tables of data and on decay curves.
• 5.2.5 — Describe the dating of objects using carbon-14.
• 5.2.5 — Explain how the type of radiation emitted and the half-life of an isotope determine which isotope is used in smoke alarms, food irradiation, sterilisation of equipment, thickness measurement and control, and the diagnosis and treatment of cancer.
• 5.2.6 — State the effects of ionising nuclear radiations on living things, including cell death, mutations and cancer.
• 5.2.6 — Explain how radioactive materials are moved, used and stored safely, with reference to exposure time, distance and shielding.

Why it matters: this is the section where vague answers fail hardest. "Be careful" and "wear protective clothing" earn nothing. Every precaution you give must be attached to a quantity you are changing: the time of exposure, the distance from the source, or the material between the source and the person.

Nuclear Model

The nuclear model of the atom describes an atom as a very small, positively charged nucleus containing nearly all the atom's mass, with negatively charged electrons in orbit around it and most of the atom's volume empty space.

Nucleon Number

The nucleon number A, also called the mass number, is the total number of protons and neutrons in the nucleus of an atom.

Proton Number

The proton number Z, also called the atomic number, is the number of protons in the nucleus of an atom. It determines which element the atom is.

Radioactivity

Radioactivity is the spontaneous and random emission of alpha particles, beta particles and/or gamma radiation from unstable nuclei.

Alpha Particle

An alpha particle consists of two protons and two neutrons, that is a helium nucleus. It has relative charge plus two, is the most strongly ionising of the three radiations and the least penetrating.

Gamma Radiation

Gamma radiation is a high-frequency electromagnetic wave emitted from a nucleus. It has no charge and no mass, is the least ionising of the three radiations and the most penetrating.

Chain Reaction

A chain reaction occurs when neutrons released by one fission are absorbed by further fissionable nuclei, causing further fissions, so that the process sustains itself.

Nuclide

A nuclide is a particular species of nucleus, specified by its nucleon number A and its proton number Z, and written in nuclide notation as A over Z followed by the chemical symbol.

Nuclear Fission

Nuclear fission is the process in which a heavy nucleus such as uranium-235 absorbs a neutron, becomes unstable and splits into two daughter nuclei, releasing energy and two or more neutrons.

Radioactive Decay

A change in an unstable nucleus that can result in the emission of alpha particles or beta particles and/or gamma radiation. The change is spontaneous, meaning it is not triggered by anything outside the nucleus, and random, meaning it cannot be predicted which nucleus will decay next or when. Every decay equation must balance twice over: the total nucleon number A is the same on both sides, and the total proton number Z is the same on both sides.

Background Radiation

Background radiation is the ionising radiation that is present in the environment at all times, detected even when no radioactive source has been deliberately introduced.

Isotope

Isotopes are atoms of the same element that have the same proton number but different numbers of neutrons, and therefore different nucleon numbers. An element may have more than one isotope.

Beta Particle

A beta particle is a high-speed electron emitted from the nucleus of an unstable atom. It has relative charge minus one and a very small mass, and has moderate ionising effect and moderate penetrating power.

Radiation Safety Precautions

Ionising nuclear radiation harms living things by removing electrons from atoms in cells, causing cell death, mutations that may be inherited, and cancer. Dose is reduced in three ways, and a precaution only counts if it names one of them: reduce the exposure time, increase the distance between the source and living tissue, and use shielding of a material thick enough to absorb the radiation emitted.

Ionising Radiation

Ionising radiation is radiation with enough energy to remove electrons from atoms, forming ions. Alpha particles, beta particles and gamma radiation are all ionising, which is why they can damage living cells.

Nuclear Fusion

Nuclear fusion is the formation of a larger nucleus by combining two smaller nuclei, with the release of energy. It is the energy source for stars.

Half-Life

The half-life of a particular isotope is the time taken for half the nuclei of that isotope in any sample to decay. It is constant for that isotope whatever the sample size, so the count rate and the number of undecayed nuclei halve every half-life.

• Error Repair Common-Mistake Clinic Twenty-three errors, each with the reason it is wrong, the model that replaces it, a sentence you can safely write in an examination, and a check. The wrong statements are quoted so that you recognise them; every quoted misconception below is false. The full misconception register for Topic 5 The false claim Why it is wrong, and the corrected model Exam-safe sentence Retrieval check 1. "Most alpha particles hit the nucleus." It contradicts the primary observation, and misdescribes the mechanism. Deflection is caused by electrostatic repulsion at a distance between two positive charges, not by contact. Almost no alpha particle comes near a nucleus. "Most alpha particles passed straight through undeflected; a very small number were deflected through large angles because they passed close to a nucleus." Name the force and its sense. Electrostatic; repulsive. 2. "The nucleus occupies most of the atom." If it did, most alpha particles would be deflected. They were not. The nucleus is roughly \(10^{4}\) to \(10^{5}\) times smaller in diameter than the atom, though it holds nearly all the mass. "Most of the atom is empty space; the nucleus is very small but contains nearly all the mass." If the nucleus were larger, would large-angle deflections be more or less common? More. 3. "Electrons and protons have equal mass." Charge and mass are independent properties. The charges are equal and opposite; the masses differ by a factor of roughly \(1840\). "The proton and electron have equal and opposite relative charges, but the electron's relative mass is only about \(1/1840\)." Why does beta deflect more than alpha in the same field? Far smaller mass, so far larger acceleration. 4. "Isotopes have different proton numbers." Different proton number means a different element. Isotopes share \(Z\) and differ in \(N\), and therefore in \(A\). "Isotopes are atoms of the same element with the same proton number but different numbers of neutrons." Are \({}^{40}_{18}\mathrm{Ar}\) and \({}^{40}_{20}\mathrm{Ca}\) isotopes? No — different elements. 5. "An ion forms by changing its nucleus." Ion formation is entirely an electron event. The nucleus is bound far too tightly for ordinary chemical or electrostatic processes to change it. \(Z\) and \(A\) are unchanged. "An atom becomes a positive ion by losing electrons and a negative ion by gaining electrons; the nucleus is unchanged." \({}^{27}_{13}\mathrm{Al}^{3+}\): protons, neutrons, electrons? 13, 14, 10. 6. "Radioactive decay can be triggered on demand." Decay is spontaneous. Heating, cooling, compressing, dissolving or chemically reacting a source does not start, stop or alter it. "Radioactive decay is spontaneous: it is not caused or controlled by anything outside the nucleus." A source is heated to \(300\ ^{\circ}\mathrm{C}\). Effect on its activity? None attributable to the heating. 7. "An individual nucleus's decay time can be predicted." Decay is random. Every nucleus of a nuclide has the same fixed chance of decaying in the next interval, regardless of how long it has already survived. Only the large sample is predictable. "The decay of an individual nucleus is random and cannot be predicted, but the behaviour of a large sample is statistically predictable." Give both halves of that sentence from memory. Individual random; population predictable. 8. "Background radiation can be ignored." Background does not decay with the source and does not vanish when the source is removed. Leaving it in adds a fixed offset to every reading, which distorts anything based on halving. "The background count rate was measured with the source removed and subtracted from each reading to give the corrected count rate." Corrected \(200\), background \(20\). Counter reading after two half-lives? \(50 + 20 = 70\). 9. "Alpha is the most penetrating radiation." It swaps the two rankings. Alpha is the most ionising, which is precisely why it is the least penetrating — it loses its energy within a few centimetres. "Alpha is the most strongly ionising and the least penetrating; it is stopped by paper or a few centimetres of air." Unaffected by paper, stopped by \(3\ \mathrm{mm}\) of aluminium. Which radiation? Beta. 10. "Gamma is completely stopped by thin lead." Gamma is absorbed gradually: each extra thickness removes a further fraction of what remains. Thin lead removes very little; even thick lead reduces rather than eliminates. "Thick lead or concrete greatly reduces the intensity of gamma radiation; it is not completely absorbed." Is a thin lead sheet adequate gamma shielding? No — only a small fraction is absorbed. 11. "Penetration and ionisation mean the same thing." They are different quantities: ionisation counts ions produced per unit distance; penetration measures how far the radiation gets before absorption. They happen to run in opposite orders. "Gamma has the weakest ionising effect but the greatest penetrating power, so it passes through packaging while alpha cannot." Which property makes alpha dangerous inside the body? Its strong ionising effect. 12. "A beta particle is an orbital electron that escaped." The nucleus contains no electrons, and beta emission changes the nucleus — \(Z\) rises by one. Losing an orbital electron would leave \(Z\) unchanged and simply make a positive ion. "In beta decay a neutron in the nucleus changes into a proton and an electron; the electron is emitted as the beta particle." If beta were an orbital electron, what would happen to \(Z\)? Nothing — contradicting the observed change of element. 13. "Gamma emission changes \(A\) or \(Z\)." Gamma radiation carries no nucleons and no charge, so there is nothing in either ledger row for it to alter. The nucleus loses energy only. "In gamma emission neither the nucleon number nor the proton number changes; the nucleus loses excess energy." Alpha then gamma: total change in \(A\) and \(Z\)? \(-4\) and \(-2\). 14. "Deflection directions in a field diagram can be assigned freely." The direction is fixed by the field, not by the person drawing. "Alpha goes left" means nothing until the plate polarity or field direction is on the diagram. "With the upper plate positive, the alpha is deflected downwards towards the negative plate and the beta upwards towards the positive plate, and further because its mass is much smaller." Swap the plate polarities. What changes? Both charged paths reverse; gamma still goes straight. 15. "The moderator absorbs neutrons to control the reactor." That is the control rods' job. If the moderator absorbed the neutrons there would be nothing left to sustain the chain reaction. "The moderator slows the neutrons so that they are more likely to cause further fission." Raise the control rods: what happens? Fewer neutrons absorbed, so the reaction rate rises. 16. "Control rods slow neutrons." The mirror image of error 15, and equally costly. Slowing neutrons would increase the fission rate — the opposite of what control rods are for. "Control rods absorb neutrons; lowering them into the core reduces the rate of the chain reaction." Match the verbs: slows / absorbs / transfers energy away. Moderator / control rods / coolant. 17. "Fission and fusion are identical." They run in opposite directions. Fission splits one heavy nucleus; fusion joins two light ones. Only "energy is released" is shared. "Fission is the splitting of a heavy nucleus after it absorbs a neutron; fusion is the joining of two small nuclei into a larger one." Which one produces the neutrons that sustain a chain reaction? Fission. 18. "Half the sample's mass disappears each half-life." Half the undecayed nuclei of that isotope decay. They become daughter nuclei, which are still in the sample. Nothing disappears. "Half-life is the time for half the nuclei of that isotope in the sample to decay; the daughter nuclei remain in the sample." After one half-life, has the sample lost half its mass? No. 19. "The raw count rate always halves." The raw reading is source plus background. Only the source part decays, so the raw reading falls towards the background level, not towards zero, and successive raw halvings take longer and longer. "Background was subtracted from each reading before the half-life was determined, because only the corrected count rate halves." Background \(30\), corrected \(240\), \(T_{1/2} = 4\ \mathrm{h}\). Counter reading at \(8\ \mathrm{h}\)? \(90\). 20. "After a few half-lives no nuclei remain." Each half-life halves what is left, and half of something is never nothing. After \(10\) half-lives about \(0.1\%\) of the original undecayed nuclei remain. "The activity continues to halve and approaches zero, but does not reach exactly zero after a finite number of half-lives." Fraction after \(5\) half-lives? \(\tfrac{1}{32}\), about \(3.1\%\). 21. "Food irradiation makes the food radioactive." The food is irradiated, not contaminated. The source stays outside; no radioactive material is added to the food. "The food is exposed to gamma radiation which kills bacteria; the food does not become radioactive, because no radioactive material is added." Is a patient radioactive after an X-ray? No — irradiated, not contaminated. 22. "External alpha radiation is always harmless." "Less penetrating" is not "harmless". Alpha can damage the eye and exposed tissue it does reach, and direct handling risks contamination, which converts a low external hazard into a high internal one. "An alpha source is a relatively low hazard from outside the body because alpha is absorbed by air and by the outer layer of skin, but alpha-emitting material inside the body is especially damaging." Why does preventing ingestion matter more than shielding for an alpha emitter? Shielding already handles the external hazard; nothing helps once it is inside. 23. "A radioactive source can be described as completely safe." Ionising radiation carries risk at any dose reaching living tissue, and the risk of effects such as cancer rises with dose. "Safe" is an absolute the physics does not support. "The precautions reduce the dose received to a very low level, so the risk is small; the source is not without risk." Rewrite "gamma is dangerous, alpha is safe". "Gamma is the greater external hazard, alpha the greater internal one; neither is without risk."

• Command Words Examiner-Language Guidance The command word tells you the shape of the answer required. Getting the shape wrong leaves the question unanswered even when the physics is right — a beautiful explanation does not answer "State" if it never states the thing. Command words as they apply to Topic 5 Command wordWhat the answer must containWorked shape from this topic StateThe fact, expressed in clear terms. No justification is asked for, so do not spend time on one."State the relative charge of an alpha particle." → "\(+2\)." Do not write a paragraph. DefineThe formal definition, in the standard wording, including every qualifying phrase."Define half-life." → "The time taken for half the nuclei of that isotope in any sample to decay." Dropping "of that isotope" weakens it. DescribeWhat happens, in the right order. No causes required unless asked."Describe the process of fission." → a nucleus such as U-235 absorbs a neutron, becomes unstable, splits into two daughter nuclei, releasing energy and two or more neutrons. ExplainCause and mechanism, not just outcome. Look for the word "because" in your own answer — if it is missing, you have probably described rather than explained."Explain why beta deflects more than alpha." → "Because its mass is far smaller, so the same order of force produces a much larger acceleration." CalculateWorking, substitution, answer, unit. Show the relationship before the numbers."Calculate the corrected count rate." → show both rates in the same unit, then the subtraction, then the answer with its unit. DetermineUsually means "get it from the data or the graph". Show which values you read off and where."Determine the half-life from the graph." → mark the two points used and show the time interval between them. IdentifyThe name of the thing: naming, selecting or recognising it is what is asked for. Quoting the evidence you used is good practice and is what a follow-up "explain" would want."Identify the radiation." → "Beta — the corrected rate was unchanged by paper but fell to zero with \(3\ \mathrm{mm}\) of aluminium." SuggestApply known physics to a situation you have not been taught directly. There may be more than one acceptable answer, but it must be justified."Suggest why a shorter half-life is preferred for a substance given to a patient." → the activity falls away soon after the procedure, limiting the patient's continuing exposure. CompareStatements about both things, on the same property. "A is strong" is not a comparison."Compare alpha and gamma." → "Alpha is more strongly ionising than gamma, but gamma is far more penetrating than alpha." DeduceA conclusion drawn from the information available, together with the step in the data that forces it. Do not assert the conclusion on its own."Deduce the daughter nuclide." → subtract \(4\) from \(A\) and \(2\) from \(Z\), then name the element that has that proton number. Phrase bank: what to write, and what to avoid writing Replace the left column with the right column Avoid — vague or wrongWrite instead — precise and creditableWhy "Alpha is the strongest.""Alpha is the most strongly ionising and the least penetrating.""Strong" does not name a property, and the two properties run in opposite orders. "Lead stops gamma.""Thick lead greatly reduces the intensity of gamma radiation."Gamma is absorbed gradually; "stops" is an overstatement. "The count rate halves.""The corrected count rate halves."The raw reading falls towards background, not towards zero. "Be careful with the source.""Handle it with tongs to increase the distance, and return it to its shielded container immediately to reduce the exposure time."A precaution scores when it names the quantity being changed. "The atom loses a proton to become an ion.""The atom loses an electron to become a positive ion; the nucleus is unchanged."Ion formation is an electron event. "The nucleus splits into two identical halves.""The nucleus splits into two daughter nuclei, which are usually of unequal size and are not the same every time."Fission products vary between events. "Radiation is dangerous.""Ionising radiation can cause cell death, mutations and cancer, and the risk increases with the dose received."Name the effects and the dependence. "The source ran out.""The activity fell until the corrected count rate was too small to measure reliably against the background."Sources do not run out; their activity falls. "It gets deflected in the field.""With the upper plate positive, it is deflected downwards towards the negative plate."A direction is meaningless without a defined field. "Half the atoms disappear.""Half the nuclei of that isotope decay, forming daughter nuclei which remain in the sample."Nothing disappears; it changes. Before you write a single Topic 5 sentence, ask three things: which particle or emission am I talking about; which property am I using (ionising, penetrating, charge, mass, half-life); and which number changed (\(A\), \(Z\), corrected count rate, time)? An answer that names all three is almost always creditable. An answer that names none of them almost never is.