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The nuclear atom, isotopes, alpha, beta and gamma decay, half-life, fission and fusion, and how radiation is used safely in industry, medicine and power stations. Each section follows one lesson: what you need to know, key terms, the equations with units, a worked example, common mistakes and an exam tip.
1 Fission & the Nucleus
What you need to know
Inside the Atom
- In the alpha scattering experiment most alpha particles went straight through a thin gold foil, and a very few bounced back by more than 90°.
- So an atom is mostly empty space, with a tiny, dense, positive nucleus that holds almost all its mass. Electrons orbit far outside it. This nuclear model replaced the plum-pudding model, in which the positive charge was spread through the atom.
- An atom is about 10−10 m across; its nucleus is less than 1/10 000 of that.
The Nucleus
- The nucleus holds protons (relative charge +1, relative mass 1) and neutrons (charge 0, mass 1). Electrons (charge −1, mass about 1/1840) orbit outside.
- The proton number Z fixes the element. The nucleon number A counts protons plus neutrons, so the number of neutrons is N = A − Z. A nuclide is written AZX.
- A neutral atom has as many electrons as protons. An ion has gained or lost electrons, so it is charged; its nucleus is unchanged.
Isotopes
- Isotopes of an element have the same number of protons but different numbers of neutrons, so the same Z and a different A.
- Isotopes have the same chemistry but a different mass; some isotopes are stable and others are radioactive. Carbon-12 and carbon-14 both have 6 protons; carbon-14 has 2 more neutrons.
Fission
- In nuclear fission a heavy nucleus such as uranium-235 or plutonium-239 absorbs a slow neutron and splits into two smaller nuclei (the daughter nuclei), releasing 2 or 3 neutrons and energy, much of it as kinetic energy of the products and some as gamma rays.
- In every nuclear equation the nucleon numbers balance on both sides, and so do the proton numbers. A neutron is written 10n.
- Fission rarely happens by itself: it is usually started by absorbing a neutron.
Chain Reaction
- The neutrons from one fission can split more nuclei, which release more neutrons: a chain reaction.
- The chain keeps going if each fission causes at least one more, on average. If too many neutrons escape or are absorbed, it dies out. A reactor keeps the chain controlled; a nuclear weapon does not.
Key terms
- Nucleus
- the tiny, dense, positive centre of an atom, made of protons and neutrons
- Proton number (Z)
- the number of protons in the nucleus; it fixes the element
- Nucleon number (A)
- the number of protons plus neutrons in the nucleus
- Isotopes
- atoms of the same element with different numbers of neutrons
- Nuclear fission
- the splitting of a heavy nucleus into two smaller nuclei, releasing neutrons and energy
- Chain reaction
- neutrons from each fission causing further fissions
Equations
| Equation | What it says, symbols and units |
|---|---|
N = A − Z | The number of neutrons is the nucleon number minus the proton number.
|
ΣA before = ΣA after, ΣZ before = ΣZ after | In any nuclear equation the top numbers balance and the bottom numbers balance. |
Diagram to know
Alpha scattering: a beam of alpha particles aimed at a thin gold foil. Draw most paths going straight through, a few bent slightly as they pass near a nucleus, and one turned back by more than 90° after a near head-on approach.
Worked example
Complete the fission equation 23592U + 10n → 9037Rb + 14455Cs + ? 10n. How many neutrons are released, and how many neutrons are in the caesium nucleus?
- Nucleon numbers on the left: 235 + 1 = 236.
- The two daughter nuclei hold 90 + 144 = 234 nucleons, so 236 − 234 = 2 neutrons are released.
- Check the proton numbers: left 92 + 0 = 92; right 37 + 55 + 0 = 92. They balance.
- Caesium-144: N = A − Z = 144 − 55 = 89 neutrons.
Answer: 2 neutrons are released; the caesium nucleus has 89 neutrons.
Common mistakes
- Saying the alpha particles bounced back off electrons. They were turned back by the positive nucleus.
- Swapping A and Z: the top (larger) number is the nucleon number, the bottom one the proton number.
- Saying isotopes have different numbers of protons. They differ only in neutrons.
- Forgetting the neutron that starts the fission when balancing the equation.
Exam tip
When asked what the scattering experiment showed, give one conclusion per observation: most went straight through, so the atom is mostly empty space; a few bounced back, so the nucleus is tiny, dense and positive. Each pair is a separate mark.
AP Physics and NGSS: NGSS (HS-PS1-8) asks for simple models of fission, fusion and decay that show the numbers of protons and neutrons are conserved. AP Physics 2 (not AP 1) treats nuclear reactions with binding energy.
2 Bohr's Atom and the Neutron
What you need to know
Orbits and the Missing Mass
- Each model of the atom lasted until evidence did not fit it: the plum-pudding model fell to alpha scattering, the plain nuclear model to the sharp lines in hydrogen's light, and a nucleus of protons alone to the mass of helium.
- Bohr (1913) placed electrons in orbits at set distances from the nucleus, called shells or energy levels.
- A helium nucleus has the charge of 2 protons but the mass of 4. In 1932 Chadwick found the neutron: no charge and about the mass of a proton, which accounts for the missing mass.
Electrons Jump
- Electrons can sit only at set energy levels. An electron moves to a higher level when it absorbs electromagnetic radiation of exactly the energy of the gap; it falls back by giving out radiation of that same energy.
- Each drop gives one sharp line in the spectrum, so every element has its own pattern of lines. A brighter lamp of the wrong energy is more photons, not bigger ones, so it is still not absorbed.
- If an atom loses an outer electron it becomes a positive ion: this is ionisation.
Key terms
- Energy level
- one of the set energies an electron in an atom can have
- Neutron
- an uncharged particle in the nucleus with about the mass of a proton
- Ionisation
- removing (or adding) an electron, so an atom becomes an ion
- Scientific model
- a description that explains the evidence and changes when new evidence does not fit
Equations
| Equation | What it says, symbols and units |
|---|---|
Ephoton = Eupper − Elower | A photon absorbed or given out carries exactly the gap between two energy levels.
1 eV = 1.6 × 10⁻¹⁹ J. The calculation goes beyond IGCSE and GCSE, which need only the idea. |
Diagram to know
An energy-level ladder for hydrogen: horizontal lines at −13.6, −3.40, −1.51 and −0.85 eV, with 0 eV at the top. Draw an upward arrow for absorption and a downward arrow for emission between two levels.
Worked example
In a hydrogen lamp an electron falls from the level at −0.85 eV to the level at −3.40 eV. Find the energy of the photon given out, in eV and in joules. (1 eV = 1.6 × 10−19 J)
- The electron falls, so the atom gives out the gap: E = Eupper − Elower = −0.85 − (−3.40) = 2.55 eV.
- In joules: 2.55 × 1.6 × 10−19 = 4.08 × 10−19 J. This is hydrogen's blue-green line.
Answer: 2.55 eV, which is 4.08 × 10−19 J
Common mistakes
- Thinking a brighter beam can lift an electron that a single photon of that energy cannot.
- Saying the neutron was part of the nuclear model from the start. It was found in 1932, twenty years after Rutherford's nucleus.
- Losing the minus signs on energy levels when finding a gap.
Exam tip
For a "how has the model of the atom changed" question, give the models in order with the evidence that ended each one. A list of models without the evidence gets only part of the marks.
AP Physics and NGSS: AP Physics 2 and NGSS HS-PS4-3 use photon energies (E = hf) and energy-level diagrams quantitatively; AP Physics 1 does not cover atomic structure.
3 Radioactive Decay
What you need to know
Alpha, Beta, Gamma
- An unstable nucleus gives out ionising radiation on its own: this is radioactive decay.
- Alpha (α) is a helium nucleus, 2 protons and 2 neutrons, charge +2. It is the most ionising and has the shortest range, a few cm of air.
- Beta (β⁻) is a fast electron, charge −1, made when a neutron in the nucleus turns into a proton. Gamma (γ) is an electromagnetic wave from the nucleus, with no mass and no charge; it ionises least.
- Ionising means knocking electrons off atoms. AQA also lists a neutron given out by a nucleus as a fourth kind of nuclear radiation.
Decay Equations
- In alpha decay A falls by 4 and Z by 2. In beta decay Z rises by 1 and A stays the same. Gamma emission changes neither; it carries away energy, often just after an alpha or beta decay.
- The new nucleus is often unstable too, so decays come in chains that end at a stable nucleus.
Random Decay
- Decay is random: you cannot predict which nucleus will decay next or when. Every nucleus of an isotope has the same chance of decaying each second.
- Temperature, pressure and chemical reactions do not change that chance. With very large numbers of nuclei the fraction that decays each second is steady, which is why a half-life can be predicted.
Half-Life
- Half-life is the time for half the unstable nuclei in a sample to decay, or for the activity (or count rate) to halve. Each isotope has its own half-life.
- Activity is the number of decays per second, in becquerels (Bq). A detector's count rate is only the share of decays that reach it.
- To find a half-life from a decay curve, subtract the background count rate first, then read the time for the count rate to halve. After n half-lives, (½)n of the nuclei are left.
Key terms
- Alpha particle
- a helium nucleus (2 protons, 2 neutrons) given out by a nucleus
- Beta particle
- a fast electron given out by a nucleus when a neutron becomes a proton
- Gamma ray
- high-frequency electromagnetic radiation given out by a nucleus
- Activity
- the number of nuclei that decay per second, in becquerels (Bq)
- Half-life
- the time for half the unstable nuclei, or the activity, to halve
Equations
| Equation | What it says, symbols and units |
|---|---|
AZX → A−4Z−2Y + 42He | Alpha decay: the nucleus loses 2 protons and 2 neutrons.
|
AZX → AZ+1Y + 0−1e | Beta decay: a neutron becomes a proton and an electron leaves the nucleus. |
after n half-lives, fraction left = (½)n | Half-life is the time for half the undecayed nuclei of an isotope to decay.
|
N = N0(½)t/t½ | The undecayed nuclei halve every half-life.
Works for the count rate or the activity too, once background is subtracted. |
Diagram to know
A decay curve: count rate (corrected for background) against time, falling steeply then levelling off. Mark the starting count rate, half of it and a quarter of it, and the equal time intervals between them: each is one half-life.
Worked example
A detector near a sample of iodine-131 reads 840 counts/min. The background count rate is 40 counts/min. Iodine-131 has a half-life of 8.0 days. What will the detector read 24 days later?
- Corrected count rate now = 840 − 40 = 800 counts/min.
- Number of half-lives = 24 ÷ 8.0 = 3.
- Corrected count rate after 3 half-lives = 800 × (½)³ = 100 counts/min.
- The background is still there, so the detector reads 100 + 40 = 140 counts/min.
Answer: 140 counts/min
Common mistakes
- Halving the measured count rate without subtracting background first; the background never halves, so the half-life comes out too long.
- Saying a nucleus decays faster when heated. Nothing physical or chemical changes the decay rate.
- In beta decay, changing A as well as Z. Only Z changes, by +1.
- Saying a sample has fully decayed after two half-lives. A quarter is still left.
Exam tip
When you write a decay equation, add up the top numbers and the bottom numbers on each side as a final line. If they do not balance, the examiner will not award the equation mark.
AP Physics and NGSS: AP Physics 2 adds positron decay and the exponential decay law with the decay constant. NGSS HS-PS1-8 asks for models of the changes in the nucleus during decay.
4 Why Nuclei Decay
What you need to know
The Valley of Stability
- Only a few hundred kinds of nucleus are stable. They lie in a narrow band, the valley of stability: light stable nuclei have N ≈ Z, heavy ones need extra neutrons.
- Too many neutrons: β⁻ decay, a neutron becomes a proton and an electron (Z rises by 1, A stays). Too many protons: β⁺ decay, a proton becomes a neutron and a positron is emitted (Z falls by 1, A stays). Too heavy: alpha decay. Every nucleus with more than 82 protons is unstable.
- Nuclei with far too many neutrons can emit a neutron: A falls by 1 and Z stays.
Bending Radiation
- Between charged plates, alpha bends a little towards the negative plate, beta bends much more towards the positive plate, and gamma is not deflected. A magnetic field sorts them the same way: opposite charges bend opposite ways.
- Beta bends more because it is far lighter. Alpha ionises most strongly because it has the biggest charge and moves the slowest.
- Emission is random in direction as well as in time.
Film, Tubes and Background
- Background radiation is always present. Sources include radon gas from rocks and the ground, rocks and buildings, food and drink, cosmic rays from space, and medical uses; nuclear power and weapons testing add a small amount.
- Radiation is detected with a Geiger–Müller tube and counter, which gives a count rate, or with a film badge, which darkens where radiation reaches it.
- Corrected count rate = measured count rate − background count rate.
Key terms
- Valley of stability
- the band of stable nuclei on a chart of neutron number against proton number
- Positron
- the antimatter partner of the electron: the same mass, charge +1
- Background radiation
- ionising radiation that is always around us from natural and human-made sources
- Count rate
- the number of decays a detector records per second or per minute
Equations
| Equation | What it says, symbols and units |
|---|---|
corrected count rate = measured count rate − background count rate | Subtract the background before using a count rate.
|
10n → 11p + 0−1e | What happens inside the nucleus in β⁻ decay. |
Diagram to know
Alpha, beta and gamma passing between a positive and a negative plate: alpha curving slightly towards the negative plate, beta curving more strongly towards the positive plate, gamma straight on.
Worked example
Neon-24 (Z = 10) has too many neutrons. It decays twice by the same kind of decay and ends stable. Name the decay and the stable nucleus, and find how many neutrons it has.
- Too many neutrons means β⁻ decay: Z rises by 1 each time and A stays 24.
- First decay: 2410Ne → 2411Na + 0−1e.
- Check the bottom numbers: 11 + (−1) = 10. Second decay: Z = 11 + 1 = 12, which is magnesium: 2411Na → 2412Mg + 0−1e.
- Neutrons in magnesium-24: N = 24 − 12 = 12.
Answer: Two β⁻ decays; the stable nucleus is magnesium-24, with 12 neutrons.
Common mistakes
- Bending alpha the same way as beta. They carry opposite charges, so they bend opposite ways.
- Saying alpha bends more because it has more charge. It is about 7000 times heavier, so it bends much less.
- Leaving background radiation in a count rate before comparing or halving it.
Exam tip
In a deflection question, state both the direction and the amount: "beta is deflected towards the positive plate, more than alpha, because it has a much smaller mass". The comparison is often the second mark.
AP Physics and NGSS: Positron (β⁺) decay and the chart of nuclides are AP Physics 2 and NGSS (HS-PS1-8) material; IGCSE Supplement and GCSE need the idea that decay moves a nucleus towards stability.
5 Nuclear Energy
What you need to know
Moderators and Control Rods
- In a reactor a moderator (water or graphite) slows the fast neutrons from fission so that uranium-235 absorbs them and splits more easily.
- Control rods (boron) absorb neutrons. Pushing them further in leaves fewer neutrons to cause fission, so the reaction slows. When each fission causes exactly one more, the power is steady.
- The chain reaction in a reactor is controlled; reactor fuel is only a few per cent uranium-235.
Mass and Energy
- After fission or fusion the products have slightly less mass than what went in. The missing mass has been released as energy: E = mc².
- c² is huge (9.0 × 1016 m²/s²), so a tiny loss of mass releases a very large amount of energy.
Fusion
- In nuclear fusion two light nuclei join to form a heavier nucleus, releasing energy; some of the mass becomes energy.
- Nuclei are positive and repel, so fusion needs a very high temperature and pressure. Stars, including the Sun, are powered by fusing hydrogen into helium. On Earth, magnetic fields hold the hot plasma away from the walls; no fusion plant yet gives out more energy than it takes in.
The Power Station
- In a nuclear power station, fission heats water to make steam, the steam turns a turbine, and the turbine drives a generator.
- Energy goes from the fuel's nuclear store to the thermal store of the steam, to the kinetic store of the turbine, and leaves by electricity. About a third of the heat becomes electricity; the rest heats the surroundings.
- Spent fuel stays hot and radioactive, so it is cooled in ponds, then sealed and stored.
Key terms
- Moderator
- a material that slows neutrons so they are more likely to cause fission
- Control rod
- a rod that absorbs neutrons to control the rate of fission
- Nuclear fusion
- the joining of two light nuclei into a heavier one, releasing energy
- Efficiency
- useful energy (or power) output divided by the total input
Equations
| Equation | What it says, symbols and units |
|---|---|
E = mc2 | In fission and fusion a little mass disappears and a lot of energy is released.
Calculations with it go beyond IGCSE and GCSE, which need only the idea that the lost mass is released as energy; AP Physics 2 uses it. |
efficiency = useful energy outputtotal energy input (× 100%) | The share of the input that ends up useful; the same with useful power output over total power input. Never more than 100%.
|
Diagram to know
A block diagram of a nuclear power station: reactor (fuel, moderator, control rods) → heat exchanger and steam → turbine → generator → transformer and grid, with the cooling water and condenser marked.
Worked example
A reactor gives 3000 MW of heat. The power station is 34% efficient. Find the electrical power output, the power wasted, and the electrical energy supplied in one day.
- Electrical power = 0.34 × 3000 = 1020 MW.
- Power wasted (heating the surroundings) = 3000 − 1020 = 1980 MW.
- One day = 24 × 3600 = 86 400 s.
- Energy = P × t = 1020 × 106 × 86 400 = 8.8 × 1013 J.
Answer: 1020 MW of electricity; 1980 MW wasted; 8.8 × 1013 J in one day
Common mistakes
- Saying the moderator absorbs neutrons. It slows them; the control rods absorb them.
- Mixing up fission (splitting a heavy nucleus) and fusion (joining light nuclei).
- Saying fusion is easy because the nuclei attract. They repel, which is why it needs such high temperatures.
Exam tip
When asked how control rods control a reactor, use the chain: rods lowered → more neutrons absorbed → fewer fissions → less energy released per second. Each arrow can be a mark.
AP Physics and NGSS: AP Physics 2 calculates the energy released from the mass defect with E = mc² and atomic mass units. NGSS HS-PS1-8 and HS-ESS1-1 use fusion to explain how the Sun releases energy.
6 Weapons, Shielding & Consequences
What you need to know
Shielding
- Alpha is stopped by a sheet of paper or a few cm of air. Beta is stopped by a few mm of aluminium. Gamma is only reduced, by thick lead or concrete.
- The more strongly a radiation ionises, the shorter its range.
Dose
- Dose, in sieverts (Sv), measures the harm radiation could do to the body; doses are usually in mSv or μSv. Dose = dose rate × time.
- Reduce the dose three ways: less time near the source, more distance from it, and more shielding.
- Being irradiated (radiation passes through you) does not make you radioactive. Average background in the UK is about 2.7 mSv a year; aircrew get more from cosmic rays.
Tracers
- Choose an isotope by its radiation first (can it get where it must?) and then its half-life (long enough to use, short enough to fade).
- A medical tracer such as technetium-99m gives out gamma rays, which escape the body to the camera, and has a half-life of 6 hours, so it soon fades from the patient.
Reactor Safety
- A reactor keeps its chain reaction controlled; a nuclear weapon needs an uncontrolled chain in nearly pure uranium-235 or plutonium-239, which reactor fuel cannot provide.
- After an accident such as Chernobyl, radioactive dust (fallout) is carried by the wind: that is contamination. Caesium-137 in it has a half-life of 30 years, so some areas stay closed for decades.
- Even after shutdown a reactor core keeps producing heat from the decay of fission products, so it must still be cooled.
The Pacemaker Finale
- Plutonium-238 once powered pacemakers: its alpha particles were stopped inside the capsule so their energy stayed as heat, and its 88-year half-life kept the heat steady for decades.
Key terms
- Range
- how far a radiation travels through a material before it is absorbed
- Dose
- a measure of the harm radiation could do to the body, in sieverts (Sv)
- Irradiation
- exposure to radiation from a source outside the body
- Contamination
- radioactive material getting onto or into an object or person
- Tracer
- a radioactive isotope put into a system to follow where it goes
Equations
| Equation | What it says, symbols and units |
|---|---|
dose = dose rate × time | The dose received grows in step with the time spent near the source.
|
after n half-lives, fraction left = (½)n | Half-life is the time for half the undecayed nuclei of an isotope to decay.
For a tracer, the activity left after n half-lives is the starting activity × (½)ⁿ. |
Worked example
A worker stands where the dose rate is 30 μSv/h for 12 short spells of 2 minutes each. What total dose does she receive? Is it below a 20 μSv limit for the shift?
- Time for one spell = 2 ÷ 60 h, so the dose = 30 × 2 ÷ 60 = 1.0 μSv.
- Total dose = 12 × 1.0 = 12 μSv.
- 12 μSv is below 20 μSv, so the shift is within the limit.
Answer: 12 μSv, which is within the 20 μSv limit
Common mistakes
- Saying gamma is stopped by lead. Thick lead only reduces it.
- Saying a person who has been irradiated becomes radioactive.
- Choosing a tracer for its long half-life. A long half-life keeps the patient radioactive for longer than needed.
- Leaving the time in minutes when the dose rate is per hour.
Exam tip
In a "choose the isotope" question, give two reasons, one about the type of radiation and one about the half-life, and link each to the job: "gamma, so it passes out of the body to the camera".
AP Physics and NGSS: The fall of dose rate with distance follows an inverse-square law, which goes beyond GCSE; NGSS HS-PS4-4 asks how absorbed radiation affects living tissue.
7 Radiation at Work
What you need to know
Pick the Source
- Pick a source by how far the radiation must get. Paper-thickness gauges use beta: paper absorbs some of it, so the count rate tells how thick the paper is (alpha would be stopped completely, gamma would pass almost unchanged).
- Smoke alarms use an alpha source (americium-241, half-life 432 years): alpha ionises the air so a small current flows; smoke absorbs the alpha, the current falls and the alarm sounds.
- Gamma from cobalt-60 passes through sealed packs, so it sterilises medical equipment and kills bacteria in food.
Contaminated or Irradiated?
- An irradiated object has had radiation pass through it; it does not become radioactive. A contaminated object has radioactive material on or in it, and keeps giving out radiation until the material is removed or has decayed.
- Sources are handled with tongs, kept in lead-lined boxes in a locked, labelled store, and used for as short a time as possible.
- The effects of radiation are published and checked by other scientists (peer review), which is how safety rules are set.
What Radiation Does to Cells
- Radiation ionises atoms in cells and can damage DNA. A large dose at once kills cells and causes radiation sickness.
- A badly repaired break can cause a mutation, which may lead to cancer years later; the risk grows in proportion to the dose. No dose is completely safe, so doses are kept as low as possible.
- Inside the body, alpha is the most dangerous because it ionises most strongly; outside the body, beta and gamma are more dangerous because they can reach the organs.
Key terms
- Irradiation
- exposure to radiation; the object does not become radioactive
- Contamination
- unwanted radioactive material on or inside an object
- Mutation
- a change in a cell's DNA, which can lead to cancer
- Peer review
- checking of published scientific work by other scientists
Equations
| Equation | What it says, symbols and units |
|---|---|
risk ≈ risk per sievert × total dose | For small doses the extra cancer risk grows in step with the total dose received.
The figure used is about 5% per sievert. Not a required equation; questions give the figure. |
Worked example
A worker receives 2.0 mSv a year at work for 40 years. Taking the extra risk of a fatal cancer as 5% per sievert, estimate her extra lifetime risk.
- Total dose = 40 × 2.0 = 80 mSv = 0.080 Sv.
- Extra risk = 5% × 0.080 = 0.4%.
- 0.4% is about 1 in 250.
Answer: About 0.4%, roughly 1 in 250
Common mistakes
- Saying food sterilised by gamma rays becomes radioactive.
- Choosing gamma for a paper-thickness gauge: it would pass through almost unchanged whatever the thickness.
- Saying alpha is harmless. Outside the body it is stopped by the skin, but inside it is the most damaging.
Exam tip
Learn the difference between contamination and irradiation as a pair of sentences. Questions often ask which is the greater hazard over time: contamination, because the source stays with the person.
AP Physics and NGSS: NGSS HS-PS4-4 asks students to evaluate claims about the effects of absorbed radiation on living tissue, using published evidence.
8 Radiation in Medicine & the Nuclear Choice
What you need to know
Aim at the Tumour
- External radiotherapy aims gamma beams at a tumour from many directions, so they add up only at the tumour and healthy tissue gets one beam's share.
- Internal radiotherapy places a source in or near the tumour; its short-range radiation (often beta) stays local. Iodine-131 collects in the thyroid and treats it from inside.
- A patient with a source inside is radioactive for a while, so staff keep visits short and keep their distance.
The PET Scanner
- In a PET scan the tracer (such as fluorine-18) emits positrons. Each positron meets an electron and they annihilate, turning their mass into two gamma rays travelling in opposite directions.
- The detector ring finds where the pairs of gamma rays came from. The tracer is carried on glucose, so it collects in busy cells such as many cancers.
- Fluorine-18 has a half-life of about 110 minutes, which keeps the patient's dose low but means the tracer must be made nearby.
Should We Build It?
- For nuclear power: no carbon dioxide while running, steady output whatever the weather, and very little fuel needed.
- Against: radioactive waste that stays dangerous for thousands of years, rare but serious accidents, high cost, long build times and public concern. Per unit of energy, nuclear power causes far fewer deaths than coal.
- Fusion power is not yet practical: it needs temperatures over 100 million °C.
Key terms
- Radiotherapy
- using ionising radiation to kill cancer cells
- Positron
- a particle with the mass of an electron and a charge of +1
- Annihilation
- a particle and its antiparticle meeting and turning into gamma rays
- Radioactive waste
- used fuel and materials that remain radioactive, sometimes for thousands of years
Equations
| Equation | What it says, symbols and units |
|---|---|
N = N0(½)t/t½ | The undecayed nuclei halve every half-life.
Here: activity left = activity made × (½)ⁿ, with n = time ÷ half-life. |
Worked example
A hospital makes 400 MBq of fluorine-18 (half-life 110 minutes) for a PET scan in another town. The journey and preparation take 330 minutes. What activity is left at the time of the scan?
- Number of half-lives = 330 ÷ 110 = 3.
- Activity left = 400 × (½)³ = 400 ÷ 8 = 50 MBq.
- Only an eighth is left, which is why PET tracers are made close to the scanner.
Answer: 50 MBq
Common mistakes
- Saying a single beam in radiotherapy gives the tumour the biggest dose. A beam is strongest where it enters, at the skin.
- Saying the two gamma rays in PET come from the nucleus directly. They come from the annihilation of the positron with an electron.
- Listing "nuclear power is renewable". Uranium is a finite fuel; it is low-carbon, not renewable.
Exam tip
In a six-mark "evaluate nuclear power" answer, give points on both sides and finish with a judgement that follows from them. A list of advantages and disadvantages with no conclusion rarely reaches the top band.
AP Physics and NGSS: NGSS HS-ESS3-2 asks students to evaluate competing energy solutions with cost, risk and benefit; AP Physics 2 covers annihilation through conservation of mass-energy.
Written in Physiworld's own words. The course tags come from the same mapping as the syllabus maps; equations are on the IGCSE, GCSE, AP Physics 1 and NGSS formula sheets. Values use g = 9.8 N/kg.
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