What you'll learn
Nuclear Physics forms a substantial component of CIE IGCSE Physics Paper 2 (Extended) and appears regularly in both multiple-choice and structured questions. This topic examines the structure of the atom, radioactive decay processes, half-life calculations, and the practical applications and hazards of radioactivity. Understanding nuclear equations and decay mechanisms is essential for securing marks in this frequently tested area.
Key terms and definitions
Nucleon — a particle found in the nucleus of an atom; either a proton or neutron.
Mass number (A) — the total number of protons and neutrons in the nucleus of an atom.
Atomic number (Z) — the number of protons in the nucleus of an atom; defines the element.
Isotopes — atoms of the same element with the same number of protons but different numbers of neutrons.
Radioactive decay — the spontaneous disintegration of an unstable nucleus, emitting radiation in the form of alpha, beta, or gamma rays.
Half-life — the time taken for half the nuclei in a sample of radioactive material to decay, or for the activity to fall to half its initial value.
Activity — the rate at which nuclei in a radioactive sample decay, measured in becquerels (Bq), where 1 Bq = 1 decay per second.
Background radiation — low-level ionising radiation present in the environment from natural and artificial sources.
Core concepts
Atomic structure and the nucleus
The atom consists of a small, dense nucleus surrounded by orbiting electrons. The nucleus contains:
- Protons — positively charged particles with relative mass 1 and relative charge +1
- Neutrons — neutral particles with relative mass 1 and no charge
- Electrons — negatively charged particles orbiting the nucleus with negligible mass (1/1840 of a proton) and relative charge -1
The nucleus is approximately 10,000 times smaller than the atom itself, yet contains virtually all the atom's mass. Nuclear notation represents an atom as:
$$^{A}_{Z}X$$
where X is the element symbol, A is the mass number, and Z is the atomic number.
For example, carbon-12 is written as $^{12}_{6}C$, indicating 6 protons and 6 neutrons (12 - 6 = 6).
Isotopes have identical chemical properties because they have the same number of electrons and protons, but different physical properties due to their different masses. Carbon-12 ($^{12}{6}C$) and carbon-14 ($^{14}{6}C$) are isotopes; both have 6 protons but carbon-14 has 8 neutrons instead of 6.
Types of radioactive decay and emission properties
Unstable nuclei undergo radioactive decay to become more stable. The three main types of radiation have distinct properties:
Alpha (α) particles:
- Composition: 2 protons + 2 neutrons (helium nucleus)
- Symbol: $^{4}{2}He$ or $^{4}{2}\alpha$
- Charge: +2
- Ionising power: highly ionising (strongest of the three)
- Penetrating power: stopped by paper or a few centimetres of air
- Range in air: approximately 3-5 cm
- Deflection in magnetic/electric fields: deflected towards negative plate (positive charge)
- Effect on parent nucleus: mass number decreases by 4, atomic number decreases by 2
Beta (β) particles:
- Composition: high-energy electron emitted from the nucleus when a neutron changes into a proton
- Symbol: $^{0}{-1}e$ or $^{0}{-1}\beta$
- Charge: -1
- Ionising power: moderately ionising
- Penetrating power: stopped by 3-5 mm aluminium sheet
- Range in air: approximately 20-30 cm
- Deflection in magnetic/electric fields: deflected towards positive plate (negative charge), more than alpha due to smaller mass
- Effect on parent nucleus: mass number unchanged, atomic number increases by 1
Gamma (γ) rays:
- Composition: electromagnetic radiation (high-energy photons)
- Symbol: γ
- Charge: 0
- Ionising power: weakly ionising
- Penetrating power: significantly reduced by several centimetres of lead or thick concrete; never completely stopped
- Range in air: follows inverse square law
- Deflection in magnetic/electric fields: no deflection (neutral)
- Effect on parent nucleus: mass and atomic numbers unchanged; excess energy released
Examiners frequently test the ability to identify radiation types based on penetration experiments. If radiation passes through paper but is stopped by aluminium, it must be beta radiation.
Nuclear equations
Nuclear equations must balance both mass numbers (top) and atomic numbers (bottom).
Alpha decay equation:
When radium-226 undergoes alpha decay:
$$^{226}{88}Ra \rightarrow ^{222}{86}Rn + ^{4}_{2}He$$
The mass numbers balance: 226 = 222 + 4
The atomic numbers balance: 88 = 86 + 2
Beta decay equation:
When carbon-14 undergoes beta decay:
$$^{14}{6}C \rightarrow ^{14}{7}N + ^{0}_{-1}e$$
A neutron in the nucleus converts to a proton, emitting an electron. The mass number remains 14, but atomic number increases from 6 to 7, changing the element from carbon to nitrogen.
Gamma emission:
Gamma emission often follows alpha or beta decay when the daughter nucleus has excess energy:
$$^{60}{27}Co^* \rightarrow ^{60}{27}Co + \gamma$$
The asterisk (*) indicates an excited nucleus. Gamma emission changes neither mass nor atomic number.
CIE IGCSE questions regularly require completion of nuclear equations by calculating missing mass or atomic numbers.
Half-life and radioactive decay calculations
Radioactive decay is random and spontaneous — impossible to predict which individual nucleus will decay or when, but the overall pattern follows a predictable exponential decrease.
Half-life remains constant for a given isotope regardless of:
- Temperature
- Pressure
- Chemical combination
- Amount of substance present
Calculating remaining activity or mass:
After n half-lives:
$$\text{Remaining amount} = \text{Initial amount} \times \left(\frac{1}{2}\right)^n$$
where $n = \frac{\text{total time elapsed}}{\text{half-life}}$
Decay curves:
Graphs showing activity against time produce characteristic exponential decay curves. Key features:
- The curve never reaches zero (theoretically)
- Steeper initial gradient indicates shorter half-life
- Half-life can be read from any point by finding the time taken for activity to halve
CIE examiners favour questions requiring half-life determination from graphs or tables of data.
Sources and effects of background radiation
Background radiation originates from:
Natural sources (approximately 85% of total):
- Radon gas from rocks (especially granite) — typically 50% of background
- Cosmic rays from space — increases with altitude
- Rocks and soil containing radioactive isotopes (uranium, thorium)
- Living organisms (carbon-14, potassium-40 in food)
Artificial sources (approximately 15% of total):
- Medical procedures (X-rays, radiotherapy)
- Nuclear weapons testing (historical)
- Nuclear power generation
- Industrial uses of radioactive materials
Background radiation must be measured and subtracted when conducting experiments with radioactive sources to obtain accurate readings.
Safety precautions and uses of radioactivity
Safety measures when handling radioactive sources:
- Store sources in lead-lined containers when not in use
- Handle with long tongs to maximise distance
- Never point sources at people
- Minimise exposure time
- Keep sources as far away as possible (inverse square law)
- Use appropriate shielding for the radiation type
- Monitor exposure with film badges or dosimeters
- Never eat, drink, or smoke near radioactive materials
Practical applications:
Medical uses:
- Gamma rays for sterilising surgical equipment
- Cobalt-60 gamma rays for cancer radiotherapy (kills cancer cells)
- Technetium-99m as a tracer (short half-life of 6 hours, gamma emitter)
Industrial uses:
- Beta radiation for thickness monitoring in paper/metal sheet production (consistent penetration allows automatic thickness control)
- Gamma rays for detecting cracks in metal structures or welds
- Carbon-14 dating for archaeological samples (half-life 5,730 years)
- Smoke detectors using americium-241 (alpha emitter)
Agricultural uses:
- Gamma irradiation to kill bacteria and extend food shelf-life
- Tracers with phosphorus-32 to study nutrient uptake in plants
Alpha sources are chosen for smoke detectors because alpha particles are stopped by smoke particles, triggering the alarm, but cannot penetrate the casing, making them safe for domestic use.
Nuclear fission and fusion
Nuclear fission — the splitting of a large unstable nucleus (such as uranium-235 or plutonium-239) into two smaller nuclei, releasing energy, neutrons, and gamma radiation.
Fission in nuclear reactors:
- A slow-moving neutron is absorbed by a uranium-235 nucleus
- The nucleus becomes unstable and splits into two smaller nuclei
- Energy is released as kinetic energy and gamma radiation
- Two or three neutrons are emitted
- These neutrons can trigger further fission reactions (chain reaction)
- Control rods absorb excess neutrons to maintain a steady reaction rate
- Moderator (often graphite or water) slows down neutrons to increase fission probability
Nuclear fusion — the joining of two light nuclei (typically hydrogen isotopes) to form a heavier nucleus, releasing enormous energy.
Fusion occurs in stars, including the Sun, where hydrogen nuclei fuse to form helium at temperatures of millions of degrees. Fusion requires:
- Extremely high temperatures (to overcome electrostatic repulsion between positive nuclei)
- High pressure (to force nuclei close together)
Fusion releases more energy per kilogram than fission and produces less radioactive waste, but requires conditions difficult to achieve and maintain on Earth.
Worked examples
Example 1: Nuclear equation completion
Question: Complete the nuclear equation for the alpha decay of polonium-210:
$$^{210}{84}Po \rightarrow ^{A}{Z}Pb + ^{4}_{2}He$$
Determine the values of A and Z.
Solution:
Mass number balance: 210 = A + 4, therefore A = 206
Atomic number balance: 84 = Z + 2, therefore Z = 82
Complete equation: $^{210}{84}Po \rightarrow ^{206}{82}Pb + ^{4}_{2}He$
[2 marks: 1 mark for each correct value]
Example 2: Half-life calculation
Question: A radioactive source has an initial activity of 8000 Bq. After 60 days, the activity has fallen to 1000 Bq. Calculate the half-life of the source.
Solution:
Activity falls from 8000 Bq → 4000 Bq (1 half-life)
4000 Bq → 2000 Bq (2 half-lives)
2000 Bq → 1000 Bq (3 half-lives)
Therefore 3 half-lives = 60 days
Half-life = 60 ÷ 3 = 20 days
[3 marks: 1 mark for identifying number of half-lives, 1 mark for working, 1 mark for correct answer with unit]
Example 3: Penetration and identification
Question: A scientist tests an unknown radioactive source. With no absorber, the count rate is 250 counts per minute. With paper between the source and detector, the count rate is 245 counts per minute. With 3 mm aluminium, the count rate drops to 40 counts per minute.
Background radiation is 35 counts per minute.
(a) Which type(s) of radiation does the source emit? Explain your answer. [3 marks]
(b) Explain why background radiation must be considered. [1 mark]
Solution:
(a) The source emits beta and gamma radiation. Paper stops alpha radiation completely, but the count rate only decreased by 5 counts per minute, showing minimal alpha emission or none. The significant decrease with aluminium (from 245 to 40) indicates beta radiation is present and stopped by aluminium. The remaining count (40 cpm with background of 35 cpm) shows gamma radiation is present as it penetrates aluminium.
[3 marks: 1 mark for identifying beta and gamma, 2 marks for complete explanation referencing penetration data]
(b) Background radiation contributes to all measurements, so must be subtracted to find the true count rate from the source alone.
[1 mark]
Common mistakes and how to avoid them
Mistake: Confusing mass number with atomic number in nuclear equations. Students write the atomic number at the top and mass number at the bottom.
Correction: Mass number (A) always goes on top (larger number), atomic number (Z) always goes on bottom. Remember: A = Z + N (number of neutrons).
Mistake: Stating that half-life is the time for all the radioactive nuclei to decay.
Correction: Half-life is the time for half the nuclei to decay, or for the activity to fall to half its initial value. After one half-life, 50% remains; after two half-lives, 25% remains.
Mistake: Treating radioactive decay as a linear process, assuming that after two half-lives nothing remains.
Correction: Decay follows an exponential pattern. The amount remaining halves with each successive half-life: $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, $\frac{1}{16}$... Theoretically, the material never completely disappears.
Mistake: Writing beta particles as $^{0}{+1}e$ instead of $^{0}{-1}e$.
Correction: Beta particles are electrons emitted from the nucleus, carrying a negative charge (-1), so the atomic number is -1.
Mistake: Stating that gamma rays have no penetrating power or are completely stopped by lead.
Correction: Gamma rays have the highest penetrating power of the three radiation types. Lead and thick concrete significantly reduce gamma intensity but never stop it completely.
Mistake: Forgetting to subtract background radiation in experiments.
Correction: Always measure and subtract background count before calculating the source's true activity. Corrected count rate = measured count rate - background count rate.
Exam technique for Nuclear Physics
Nuclear equations: Questions using "determine" or "calculate" require you to show balancing of both mass and atomic numbers. Write out the balance equations explicitly (e.g., "226 = 222 + 4") for method marks even if your final answer is incorrect.
Half-life problems: When asked to "calculate" half-life from data, show the number of half-lives clearly. Drawing a simple diagram showing successive halvings helps structure your answer and reduces arithmetic errors. Include units (hours, days, years) in your final answer.
Explaining safety precautions: Use specific physics principles (inverse square law, penetration properties, ionisation) rather than general statements. "Use tongs to increase distance because radiation intensity decreases with distance" scores marks; "be careful" does not.
Describing applications: Link the choice of radiation type to its properties. For example: "Beta radiation is used for thickness monitoring because it partially penetrates the material, allowing consistent measurement" demonstrates understanding worth full marks.
Quick revision summary
Nuclear Physics covers atomic structure (protons, neutrons, electrons), with the nucleus containing nucleons. Radioactive decay produces alpha particles (helium nuclei, stopped by paper), beta particles (electrons, stopped by aluminium), or gamma rays (electromagnetic radiation, reduced by lead). Nuclear equations must balance mass and atomic numbers. Half-life is the time for half the nuclei to decay, following an exponential pattern. Background radiation exists from natural and artificial sources. Applications include medical tracers, radiotherapy, thickness gauging, and sterilisation. Safety requires distance, shielding, and minimising exposure time. Fission splits heavy nuclei; fusion joins light nuclei, both releasing energy.