IGCSE Physics · Unit 5: Nuclear Physics · Core + Extended
Nuclear Physics CoreExtended adds fission/fusion, decay equations & half-life calculations
This note covers what’s inside an atom, the three types of radiation an unstable nucleus can emit, how radioactive decay changes a nucleus over time, and the safety precautions that make working with radioactive sources possible. It’s a shorter unit than some of the others, but the ideas here — especially nuclide notation and half-life — reward careful, methodical practice.
Why this matters
Nuclear physics questions are very “notation-heavy” — once you’re fluent in reading and writing nuclide symbols, most of this unit becomes applying a small number of rules consistently, rather than learning lots of new content.
1. The Atom
An atom consists of a tiny, positively charged nucleus at its centre, surrounded by negatively charged electrons in orbit around it. Atoms are normally neutral overall (equal numbers of protons and electrons), but can become charged ions: losing electrons produces a positive ion; gaining electrons produces a negative ion.
Alpha particle scattering — evidence for the nuclear model Extended
In the famous alpha-scattering experiment, a beam of alpha particles was fired at a very thin sheet of metal. Most alpha particles passed straight through with little or no deflection, but a small number were deflected through large angles, and a tiny number bounced almost straight back. This provided evidence that:
(a) the atom’s nucleus is very small, surrounded mostly by empty space (since most alpha particles passed straight through undisturbed);
(b) the nucleus contains most of the atom’s mass (since only a very small, dense, massive nucleus could deflect a fast-moving alpha particle back the way it came);
(c) the nucleus is positively charged (since alpha particles, which are positive, were repelled/deflected by it).
(a) the atom’s nucleus is very small, surrounded mostly by empty space (since most alpha particles passed straight through undisturbed);
(b) the nucleus contains most of the atom’s mass (since only a very small, dense, massive nucleus could deflect a fast-moving alpha particle back the way it came);
(c) the nucleus is positively charged (since alpha particles, which are positive, were repelled/deflected by it).
2. The Nucleus
The nucleus is made up of protons and neutrons (together called nucleons).
| Particle | Relative charge | Location |
|---|---|---|
| Proton | +1 | nucleus |
| Neutron | 0 | nucleus |
| Electron | −1 | orbiting the nucleus |
Proton number (atomic number), Z — the number of protons in the nucleus (this also equals the number of electrons in a neutral atom, and determines which element it is).
Nucleon number (mass number), A — the total number of protons and neutrons in the nucleus.
number of neutrons = A − Z
Nuclide notation writes an atom as AZX, where X is the element symbol.
Worked example — reading nuclide notation
For the nuclide ²³⁵₉₂U (uranium-235): Z = 92, A = 235.
Number of protons = 92
Number of neutrons = A − Z = 235 − 92 = 143
Number of electrons (neutral atom) = 92
Number of protons = 92
Number of neutrons = A − Z = 235 − 92 = 143
Number of electrons (neutral atom) = 92
An isotope is a form of an element with the same number of protons but a different number of neutrons — isotopes of the same element have the same Z but different A. An element may have more than one isotope.
Worked example — identifying isotopes
Carbon-12 (¹²₆C) and carbon-14 (¹⁴₆C) are both isotopes of carbon.
Both have Z = 6 (6 protons — this is what makes them both carbon).
Carbon-12 has 12 − 6 = 6 neutrons; carbon-14 has 14 − 6 = 8 neutrons.
They are isotopes because they share the same proton number but differ in neutron number (and hence nucleon number).
Both have Z = 6 (6 protons — this is what makes them both carbon).
Carbon-12 has 12 − 6 = 6 neutrons; carbon-14 has 14 − 6 = 8 neutrons.
They are isotopes because they share the same proton number but differ in neutron number (and hence nucleon number).
Nuclear fission and fusion Extended
Nuclear fission is the splitting of a large, unstable nucleus into two smaller nuclei (plus usually some neutrons), releasing energy. Nuclear fusion is the joining of two small nuclei into one larger nucleus, also releasing energy (this is the process powering the Sun). Both can be represented with a nuclide equation, and in both cases, a small amount of mass is converted into a (comparatively) large amount of released energy — though the exact values are not required at this level, just the qualitative idea that mass decreases and energy is released.
Try it — The Atom and Nucleus
- For the nuclide ²⁷₁₃Al, state the number of protons, neutrons, and electrons (as a neutral atom).
- Explain what makes two nuclides isotopes of the same element.
- Explain how the alpha particle scattering experiment provides evidence that the nucleus is positively charged.
Show answers
- Protons = Z = 13. Neutrons = A − Z = 27 − 13 = 14. Electrons (neutral atom) = 13.
- They must have the same proton number (number of protons), since this determines the element, but a different neutron number (and therefore a different nucleon number).
- Alpha particles are positively charged. Some alpha particles were deflected through large angles, or bounced almost straight back, when fired at the metal sheet — this repulsion is evidence that they encountered a concentration of positive charge (the nucleus), since like charges repel.
3. Detection of Radioactivity
Background radiation is the low-level ionising radiation that is present everywhere in the environment, from natural and artificial sources. Significant sources include: radon gas (present in the air, especially in some types of rock/soil), rocks and buildings (many contain trace radioactive elements), food and drink (naturally occurring radioactive isotopes), and cosmic rays (radiation reaching Earth from space).
Ionising nuclear radiation is measured using a detector (such as a Geiger-Müller tube) connected to a counter, giving a count rate in counts per second or counts per minute.
Correcting for background radiation Extended
Since background radiation is always present, any measurement of a radioactive source’s count rate actually includes a contribution from background radiation too. To find the count rate due to the source alone, measure the background count rate first (with no source present), then subtract it from the total count rate measured with the source present.
corrected count rate = measured count rate − background count rate
corrected count rate = measured count rate − background count rate
Worked example — correcting for background
A Geiger counter placed near a radioactive source reads 84 counts/minute. With no source present, the background reading is 12 counts/minute. Find the corrected count rate due to the source.
Corrected count rate = 84 − 12 = 72 counts/minute
Corrected count rate = 84 − 12 = 72 counts/minute
4. The Three Types of Nuclear Emission
Radiation from an unstable nucleus is emitted spontaneously (it cannot be predicted or triggered externally) and in a random direction.
| Alpha (α) | Beta (β) | Gamma (γ) | |
|---|---|---|---|
| Nature | 2 protons + 2 neutrons (helium nucleus) | a fast-moving electron | electromagnetic radiation (a high-energy wave) |
| Relative ionising effect | strong | moderate | weak |
| Relative penetrating ability | weak — stopped by paper/skin | moderate — stopped by a few mm of aluminium | strong — needs thick lead or concrete to stop |
Deflection in fields, and why ionising ability differs Extended
In electric and magnetic fields: alpha particles (positive) and beta particles (negative) are deflected in opposite directions to each other (being oppositely charged); gamma radiation (uncharged) is not deflected at all.
The relative ionising effects can be explained by kinetic energy and electric charge: alpha particles are relatively large, slow-moving, and carry a large charge (+2), so they interact strongly and frequently with atoms they pass close to, ionising them easily but losing energy quickly (hence poor penetration). Gamma radiation carries no charge, so it interacts only weakly and rarely with matter, meaning it ionises weakly but can travel much further before being absorbed (hence strong penetration). Beta particles fall in between.
The relative ionising effects can be explained by kinetic energy and electric charge: alpha particles are relatively large, slow-moving, and carry a large charge (+2), so they interact strongly and frequently with atoms they pass close to, ionising them easily but losing energy quickly (hence poor penetration). Gamma radiation carries no charge, so it interacts only weakly and rarely with matter, meaning it ionises weakly but can travel much further before being absorbed (hence strong penetration). Beta particles fall in between.
Try it — Types of Emission
- State which type of radiation (alpha, beta, or gamma) has the strongest ionising effect.
- State which type of radiation is not deflected by an electric field, and explain why.
- Explain, in terms of penetration, why alpha radiation is the easiest of the three to shield against.
Show answers
- Alpha radiation has the strongest ionising effect.
- Gamma radiation is not deflected, because it is electromagnetic radiation and carries no electric charge — an electric field only exerts a force on charged particles.
- Alpha radiation has the weakest penetrating ability of the three, being stopped by just a sheet of paper or the outer layer of skin, meaning even a thin barrier is enough to block it completely.
5. Radioactive Decay
Radioactive decay is a spontaneous, random change in an unstable nucleus, resulting in the emission of an alpha particle, a beta particle, and/or gamma radiation. During alpha decay or beta decay, the nucleus changes into that of a different element (gamma emission alone does not change the identity of the nucleus, since no particles are ejected).
Why nuclei are radioactive, and the effect of decay Extended
Isotopes may be radioactive due to having an excess of neutrons in the nucleus, and/or simply being too heavy (having too many nucleons overall) to be stable.
Alpha, beta, and gamma emission all tend to move a nucleus toward greater stability. In particular, beta decay reduces the number of excess neutrons through the process:
neutron → proton + electron
This is why beta decay increases the proton number by 1 (a neutron converts into a proton, which stays in the nucleus, while the electron is emitted as the beta particle).
Alpha, beta, and gamma emission all tend to move a nucleus toward greater stability. In particular, beta decay reduces the number of excess neutrons through the process:
neutron → proton + electron
This is why beta decay increases the proton number by 1 (a neutron converts into a proton, which stays in the nucleus, while the electron is emitted as the beta particle).
Decay equations Extended
In a nuclide decay equation, the nucleon numbers (A) must balance on both sides, and the proton numbers (Z) must also balance on both sides. An alpha particle is written as ⁴₂He (or ⁴₂α); a beta particle is written as ⁰₋₁e (or ⁰₋₁β).
Worked example — alpha decay equation
Radium-226 (²²⁶₈₈Ra) decays by alpha emission. Write the decay equation, and identify the new element formed (radon, Rn, Z = 86).
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
Check: nucleon numbers: 226 = 222 + 4 ✓. Proton numbers: 88 = 86 + 2 ✓.
The nucleon number decreases by 4, and the proton number decreases by 2, exactly matching the alpha particle emitted.
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
Check: nucleon numbers: 226 = 222 + 4 ✓. Proton numbers: 88 = 86 + 2 ✓.
The nucleon number decreases by 4, and the proton number decreases by 2, exactly matching the alpha particle emitted.
Worked example — beta decay equation
Carbon-14 (¹⁴₆C) decays by beta emission. Write the decay equation, and identify the new element formed (nitrogen, N, Z = 7).
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Check: nucleon numbers: 14 = 14 + 0 ✓. Proton numbers: 6 = 7 + (−1) ✓.
The nucleon number stays the same (a neutron converting to a proton doesn’t change the total nucleon count), but the proton number increases by 1, since a neutron has become a proton.
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Check: nucleon numbers: 14 = 14 + 0 ✓. Proton numbers: 6 = 7 + (−1) ✓.
The nucleon number stays the same (a neutron converting to a proton doesn’t change the total nucleon count), but the proton number increases by 1, since a neutron has become a proton.
Try it — Radioactive Decay
- Explain why the nucleon number does not change during beta decay, even though a new element is formed.
- Polonium-210 (²¹⁰₈₄Po) decays by alpha emission to form lead (Pb, Z = 82). Write the balanced decay equation.
- Explain why beta decay is associated with a nucleus that has an excess of neutrons.
Show answers
- Beta decay occurs via a neutron converting into a proton and an electron (neutron → proton + electron). The proton stays in the nucleus (increasing the proton number by 1), but since a neutron is simply replaced by a proton, the TOTAL number of nucleons (protons + neutrons) stays exactly the same — it is the proton/neutron balance that changes, not the total.
- ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He (nucleon numbers: 210 = 206+4 ✓; proton numbers: 84 = 82+2 ✓)
- Beta decay converts a neutron into a proton, directly reducing the number of neutrons in the nucleus by one (and increasing protons by one) — this is exactly the process that helps a neutron-heavy nucleus move toward a more stable proton-to-neutron ratio.
6. Half-Life
The half-life of a radioactive isotope is the time taken for half of the nuclei of that isotope, in any sample, to decay.
Worked example — simple half-life calculation
A sample starts with an activity of 800 counts/minute. Its half-life is 6 hours. Find the activity after 18 hours.
18 hours = 3 half-lives (18 ÷ 6 = 3)
After 1 half-life: 800 ÷ 2 = 400
After 2 half-lives: 400 ÷ 2 = 200
After 3 half-lives: 200 ÷ 2 = 100 counts/minute
18 hours = 3 half-lives (18 ÷ 6 = 3)
After 1 half-life: 800 ÷ 2 = 400
After 2 half-lives: 400 ÷ 2 = 200
After 3 half-lives: 200 ÷ 2 = 100 counts/minute
Finding half-life from a decay curve Extended
On a graph of activity (or count rate) against time, the half-life can be read off by finding the time taken for the activity to fall to half of any chosen starting value on the curve — this should give a consistent answer no matter which starting point on the curve you choose, since each halving takes the same amount of time.
Worked example — half-life from data Extended
A sample’s activity falls from 640 counts/minute to 80 counts/minute over a period of 45 minutes. Find the half-life.
640 → 320 → 160 → 80: this took 3 halvings to go from 640 to 80.
Time for 3 half-lives = 45 minutes
Half-life = 45 ÷ 3 = 15 minutes
640 → 320 → 160 → 80: this took 3 halvings to go from 640 to 80.
Time for 3 half-lives = 45 minutes
Half-life = 45 ÷ 3 = 15 minutes
Choosing isotopes for applications Extended
The choice of isotope for a given application depends on both the type of radiation it emits and its half-life:
- Household fire (smoke) alarms: a weak alpha source with a long half-life — alpha’s short range keeps it safely contained within the detector, and a long half-life means the source doesn’t need replacing often.
- Irradiating food to kill bacteria: a strong gamma source — gamma’s high penetration reaches all the way through the food, without leaving the food itself radioactive.
- Sterilising medical equipment: gamma rays, for the same reason — strong penetration to reach every surface, including inside packaging.
- Measuring/controlling material thickness: the choice of alpha, beta, or gamma depends on the thickness and material being measured — the radiation must be able to just partially penetrate the material, so that changes in thickness produce a measurable change in the detected count rate.
- Diagnosis and treatment of cancer: gamma rays — able to penetrate the body from outside (diagnosis) or be aimed precisely at internal tumours (treatment), and gamma-emitting tracers with a short half-life are chosen for diagnosis so the radioactivity in the patient decays away quickly.
Try it — Half-Life
- A sample has an initial activity of 1200 counts/minute and a half-life of 4 days. Find its activity after 12 days.
- A sample’s activity falls from 960 counts/minute to 60 counts/minute over 80 minutes. Find its half-life.
- Explain why a gamma-emitting isotope, rather than an alpha-emitting one, is used to irradiate food.
Show answers
- 12 days ÷ 4 days = 3 half-lives. 1200 → 600 → 300 → 150 counts/minute
- 960→480→240→120→60: that’s 4 halvings in 80 minutes. Half-life = 80 ÷ 4 = 20 minutes
- Gamma radiation has a much greater penetrating ability than alpha radiation, allowing it to pass all the way through the food to kill bacteria throughout, rather than just at the surface. Alpha radiation would be absorbed within a very short distance and could not penetrate deep into the food.
7. Safety Precautions
Ionising nuclear radiation can damage living tissue, causing cell death, mutations, and potentially cancer. Radioactive materials must be moved, used, and stored safely — for example, using tongs rather than direct handling, storing sources in thick lead-lined containers, and clearly labelling radioactive materials.
Three ways to reduce exposure Extended
Safety precautions for all ionising radiation generally work by one (or more) of three principles:
Reducing exposure time — spending as little time as possible near a source.
Increasing distance — radiation intensity decreases rapidly with distance from the source, so working as far away as practical (e.g. using remote handling tools) reduces the dose received.
Using shielding — placing an appropriate absorbing material (e.g. lead for gamma radiation) between the source and the person, to absorb the radiation before it reaches them.
Reducing exposure time — spending as little time as possible near a source.
Increasing distance — radiation intensity decreases rapidly with distance from the source, so working as far away as practical (e.g. using remote handling tools) reduces the dose received.
Using shielding — placing an appropriate absorbing material (e.g. lead for gamma radiation) between the source and the person, to absorb the radiation before it reaches them.
Try it — Safety
- State two effects that ionising radiation can have on living cells.
- Explain how increasing the distance between a person and a radioactive source helps protect them.
- Suggest why lead, rather than paper, is used to shield against a gamma source.
Show answers
- Cell death, mutation, and cancer. (Any two.)
- Radiation spreads out and becomes less concentrated (intensity decreases) the further it travels from its source, so increasing the distance between a person and the source reduces the amount of radiation reaching them, lowering their exposure.
- Gamma radiation has a very high penetrating ability and is barely absorbed by a thin material like paper. Lead is dense and absorbs gamma radiation far more effectively, making it a suitable shielding material, whereas paper would let almost all the gamma radiation straight through.
Common mistakes to watch for
- Forgetting to balance BOTH the nucleon numbers (A) and the proton numbers (Z) when writing or checking a decay equation.
- Thinking gamma emission changes the identity of the element — only alpha and beta decay do this, since only they involve a particle leaving the nucleus.
- Forgetting to subtract background radiation before calculating a “corrected” count rate.
- Assuming half-life calculations only work for exact whole numbers of half-lives — always check how many half-lives have actually passed (it may not be a round number in the source data, even if the examples given here are).
- Mixing up which type of radiation is most/least ionising vs. most/least penetrating — they’re opposite: alpha is most ionising but least penetrating; gamma is least ionising but most penetrating.
- Forgetting that alpha and beta particles deflect in OPPOSITE directions in a field (being oppositely charged), while gamma is not deflected at all.
8. Quick-Fire Challenge Round
True or False?
- Gamma radiation is the most strongly ionising of the three types of nuclear emission.
- During beta decay, a neutron in the nucleus converts into a proton and an electron.
- Isotopes of the same element always have the same nucleon number.
- Increasing the distance from a radioactive source is one way to reduce a person’s exposure to radiation.
Show answers
- False — alpha radiation is the most strongly ionising; gamma is the weakest ioniser (but the most penetrating).
- True — this is exactly what happens during beta decay, and it’s why the proton number increases by 1 while the nucleon number stays the same.
- False — isotopes of the same element have the same PROTON number (Z), but different nucleon numbers (A), since they differ in their number of neutrons.
- True — radiation intensity falls off with distance, so increasing distance from the source reduces exposure.
Spot the Error
- “A sample has a half-life of 5 minutes. After 5 minutes, all of the radioactive nuclei will have decayed.”
- “Alpha particles have the greatest penetrating ability of the three types of radiation, since they carry the most charge.”
- “A nuclide equation for beta decay: ¹⁴₆C → ¹³₇N + ⁰₋₁e”
Show answers
- A half-life is the time for HALF of the nuclei to decay, not all of them. After one half-life (5 minutes), half the original nuclei remain undecayed; it would take further half-lives (in theory, infinitely many) to approach zero, though in practice the sample becomes negligible after several half-lives.
- Alpha particles actually have the WEAKEST penetrating ability of the three, despite being the most strongly ionising. Greater charge and mass make alpha particles interact very readily with matter, losing their energy (and being stopped) very quickly — this is why they ionise strongly but penetrate poorly.
- The nucleon number doesn’t balance: 14 on the left, but 13 + 0 = 13 on the right. It should be ¹⁴₆C → ¹⁴₇N + ⁰₋₁e, keeping the nucleon number at 14 on both sides.
9. Mixed Practice — Bringing It All Together
- For the nuclide ³¹₁₅P, state the number of protons, neutrons, and electrons (as a neutral atom).
- State which type of radiation is stopped by a few millimetres of aluminium.
- A source’s measured count rate is 150 counts/minute, and the background count rate is 18 counts/minute. Find the corrected count rate.
- Thorium-232 (²³²₉₀Th) decays by alpha emission to form radium (Ra, Z = 88). Write the balanced decay equation.
- A sample has an initial activity of 2000 counts/minute and a half-life of 3 hours. Find its activity after 9 hours.
Show answers
- Protons = 15, neutrons = 31 − 15 = 16, electrons = 15
- Beta radiation
- 150 − 18 = 132 counts/minute
- ²³²₉₀Th → ²²⁸₈₈Ra + ⁴₂He (check: 232 = 228+4 ✓; 90 = 88+2 ✓)
- 9 ÷ 3 = 3 half-lives. 2000 → 1000 → 500 → 250 counts/minute
Practice at Home
Parts C and D include Extended-only content.
Part A — The atom and nucleus
- State the relative charges of a proton, a neutron, and an electron.
- For the nuclide ¹⁹₉F, find the number of protons, neutrons, and electrons.
- Explain the difference between proton number and nucleon number.
Part B — Detecting radiation and types of emission
- Name two sources of background radiation.
- Copy and complete: alpha radiation is stopped by ___; beta radiation is stopped by ___; gamma radiation is stopped by ___.
- State which type of radiation is uncharged, and explain how this affects its behaviour in a magnetic field.
Part C — Decay equations and half-life (Extended included)
- A measured count rate is 220 counts/minute, with background radiation of 20 counts/minute. Find the corrected count rate.
- Americium-241 (²⁴¹₉₅Am) decays by alpha emission to form neptunium (Np, Z = 93). Write the balanced decay equation.
- A sample’s activity falls from 800 counts/minute to 25 counts/minute over 100 minutes. Find its half-life.
Part D — Applications and safety (Extended included)
- Explain why a long-half-life alpha source is suitable for use in a household smoke alarm.
- State the three general principles used to reduce a person’s exposure to ionising radiation.
- Explain why gamma-emitting isotopes with a short half-life are preferred for medical diagnostic scans.
Key Vocabulary Recap
Isotope — atoms of the same element (same proton number) with different neutron numbers
Background radiation — low-level radiation always present from natural and artificial sources
Alpha, beta, gamma — the three types of nuclear emission, differing in nature, ionising power, and penetration
Half-life — the time for half the nuclei in a sample to decay
Nuclide notation — AZX, showing nucleon number and proton number
Shielding — using an absorbing material to block radiation from reaching a person
Syllabus Reference
This note covers Cambridge IGCSE Physics (0625) section 5, Nuclear physics, in full — 5.1 The nuclear model of the atom (5.1.1 The atom, 5.1.2 The nucleus) and 5.2 Radioactivity (5.2.1 Detection of radioactivity, 5.2.2 The three types of nuclear emission, 5.2.3 Radioactive decay, 5.2.4 Half-life, 5.2.5 Safety precautions). Core and Supplement content are both included, with Extended-only material (alpha scattering evidence, fission/fusion, deflection in fields, decay equations, half-life calculations from data, isotope choice for applications, and explained safety precautions) clearly flagged throughout.
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