O Level Physics: Nuclear physics – Revision Notes (Cambridge 5054)

These notes condense topic 5, Nuclear physics, from the Cambridge O Level Physics 5054 syllabus for examination in 2026, 2027 and 2028 (sections 5.1.1 to 5.2.6). For full explanations and worked examples, read the study guide first.

After the notes, test yourself with the practice questions. The Cambridge O Level Physics hub and the printable checklist show where this topic sits in the course, and the free 10-minute diagnostics help you pick what to revise next.

Key definitions

Term	Meaning
Proton number Z	Number of protons in the nucleus (atomic number)
Nucleon number A	Number of protons plus neutrons (mass number)
Neutrons	A − Z
Nuclide	A particular nucleus with given Z and A, written ᴬ_ZX
Isotopes	Nuclei of the same element (same Z) with different A, so different neutron numbers
Positive ion	Atom that has lost electrons; negative ion has gained electrons
Count rate	Counts detected per second or per minute
Background radiation	Radiation always present from the surroundings
Corrected count rate	Count rate with the source, less the count rate from background alone
Half-life	Time for half of the nuclei of an isotope, in any sample, to decay
Fusion	Two smaller nuclei combine into a larger nucleus, releasing energy
Fission	A heavy nucleus (for example uranium-235) takes in a neutron, breaks into daughter nuclei and gives out energy plus two or more neutrons

The nuclear atom

• Positive nucleus, negative electrons in orbit around it.
• Alpha scattering from a thin foil: most pass straight through (mostly empty space); a few deflect a lot (small nucleus, positive, most of the mass); a very few return almost the way they came (a heavy nucleus repelling them).

Detection and background

Detector	Detects	What you see or hear
Cloud chamber	Alpha	Short, thick, straight tracks
Spark counter	Alpha	Sparks between charged wire and gauze
GM tube and counter	Beta and gamma	Clicks or counts

Sources of background radiation: cosmic rays, radon (a gas in the air), rocks and buildings, and what we eat and drink.

Method for corrected count rate:

1. Convert the measured counts into counts per minute (or per second).
2. Convert the background counts into the same unit.
3. Subtract background from measured.

The three emissions

	Alpha	Beta (β⁻)	Gamma
Nature	Helium nucleus: 2 protons and 2 neutrons	Electron ejected by the nucleus	Electromagnetic wave of very high frequency
Charge	Positive	Negative	None
Ionising	Strongest	Medium	Weakest
Penetrating	Least (paper, few cm of air)	Medium (few mm of aluminium)	Greatest (thick lead or concrete reduces it)
Electric field	Small bend to negative plate	Large bend to positive plate	None
Magnetic field	Bends one way	Bends the opposite way	None

Must-know distinctions:

• Ionising power and penetrating power run in opposite order.
• Emission is spontaneous (no trigger) and random (you cannot say which nucleus goes next, or in which direction the radiation leaves).
• Gamma often accompanies alpha or beta decay, takes away surplus energy and changes neither A nor Z.

Decay equations

Emission	Change in A	Change in Z
Alpha ⁴₂He	−4	−2
Beta ⁰₋₁e	0	+1
Gamma	0	0

Method in steps:

1. Write the parent nuclide on the left.
2. Write the emitted particle in nuclide notation on the right.
3. Work out the daughter’s A and Z by subtracting from the parent (top from top, bottom from bottom).
4. Look up the symbol from Z and check both totals balance.

Reminder: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He. Check: 210 = 206 + 4 and 84 = 82 + 2.

Fission, fusion and the reactor

• Fusion powers stars: hydrogen nuclei fuse to make helium.
• Fission of U-235: neutron absorbed, nucleus splits into two daughter nuclei, two or more neutrons released, energy released.
• Chain reaction: the released neutrons cause further fissions.

Reactor part	Job
Moderator	Slows neutrons so they can be absorbed
Control rods	Absorb neutrons; in to reduce power, out to raise it
Coolant	Carries thermal energy out of the core to make steam

Steady power means one neutron from each fission causes exactly one further fission on average.

Half-life

Method in steps:

1. Correct for background if readings are measured values.
2. Find how many times the rate has halved: number of half-lives n = total time ÷ half-life.
3. Final value = starting value ÷ 2ⁿ.
4. From a table or curve, choose a value, find half of it, read the time gap, and check with a second pair.

Small reminder: 720 counts per minute with half-life 5 minutes becomes 360 after 5 minutes, 180 after 10, 90 after 15 and 45 after 20.

Carbon-14 dating

• Living things take in carbon-14, so the proportion stays constant while alive.
• Once dead, intake stops and the carbon-14 left decays (half-life 5730 years).
• Compare the activity of the object with that of living material: half the activity means one half-life of 5730 years.

Choosing an isotope for a use

Use	Radiation	Reasoning
Smoke alarm	Alpha	Ionises air; smoke blocks it, current falls; safe because alpha is easily stopped; long half-life
Food irradiation	Gamma	Penetrates food and packaging to kill bacteria
Sterilising equipment	Gamma	Passes through sealed packs
Thickness control	Beta for thin sheet, gamma for thick metal	Must be partly absorbed; long half-life for steady readings
Cancer diagnosis	Gamma tracer	Detected outside the body; short half-life so it soon disappears
Cancer treatment	Gamma beam	High dose to tumour, aimed from several directions

Safety

• Effects of ionising radiation: cell death, mutations, cancer.
• Reduce exposure time, increase distance (use tongs), use shielding (lead-lined containers, thick walls).

Worked reminders

• Neutron count: ⁶⁵₂₉Cu has 65 − 29 = 36 neutrons. Its isotope ⁶³₂₉Cu has 34.
• Two-step decay: ²³⁸₉₂U emits alpha to give ²³⁴₉₀Th, which emits beta to give ²³⁴₉₁Pa.
• Fission balance: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n. Top: 236 on each side. Bottom: 92 on each side.
• Carbon-14 age: one quarter of the original activity is two half-lives, so 2 × 5730 = 11 460 years.
• Corrected rate: 156 counts in 2 minutes is 78 per minute; background of 18 counts in 3 minutes is 6 per minute; corrected rate 72 per minute.

Self-test

1. Find the number of neutrons in a nucleus of ⁵⁶₂₆Fe.
2. A sulfur atom has 16 protons. How many electrons does an S²⁻ ion have?
3. Lithium has isotopes with nucleon numbers 6 and 7 and proton number 3. State the neutron number of each.
4. Complete: ²¹⁰₈₄Po decays by alpha emission to a nuclide with what A and Z?
5. A GM tube measures 95 counts per minute with a source and 11 counts per minute without it. What is the corrected count rate?
6. An isotope has a half-life of 5 minutes. A sample gives a corrected 720 counts per minute. What is the rate after 20 minutes?
7. ⁶⁰₂₇Co emits a beta particle. What is the proton number of the daughter?
8. Which of the three radiations is not deflected by an electric field?
9. A corrected count rate falls from 960 to 120 counts per minute in 18 hours. What is the half-life?
10. Give two reasons a short half-life suits a gamma tracer used to diagnose illness.
11. State three precautions when handling a radioactive source.
12. In the alpha-scattering experiment, what does the very small number of particles bouncing almost straight back suggest?

Answers

1. 56 − 26 = 30 neutrons.
2. 16 electrons in the atom plus 2 gained = 18 electrons.
3. 6 − 3 = 3 neutrons and 7 − 3 = 4 neutrons.
4. A = 210 − 4 = 206 and Z = 84 − 2 = 82 (lead).
5. 95 − 11 = 84 counts per minute.
6. Four half-lives (20 ÷ 5), so 720 ÷ 16 = 45 counts per minute.
7. 27 + 1 = 28 (nickel).
8. Gamma radiation.
9. 960 to 480 to 240 to 120 is three half-lives, so 18 ÷ 3 = 6 hours.
10. The patient receives a smaller total dose, and the tracer is gone from the body soon after the scan. Gamma also passes out of the body so it can be detected.
11. Any three of: keep exposure time short, keep as far away as possible (use tongs), keep it in a lead-lined container, do not point it at people.
12. A very small, dense, positively charged nucleus that holds most of the atom’s mass repelled them.

Where marks are usually lost

• Calling alpha the most penetrating, or beta the most ionising.
• Swapping the roles of control rods and moderator.
• Using measured counts, not corrected counts, when finding a half-life.
• Putting A and Z the wrong way round in a nuclide symbol.
• Writing “the nucleus is dense” without evidence from particles bouncing back.
• Not saying that the neutron must first be absorbed in fission.
• Forgetting that beta emission raises Z by one.
• Choosing alpha for a thickness gauge or gamma for a smoke alarm without justifying it with penetration and ionisation.
• Saying radiation “leaks” in the safety answer instead of naming time, distance or shielding.

Frequently asked questions

How do you find a half-life from count rate readings? Subtract the background count rate from each reading first, then find the time for the corrected count rate to halve. Using measured counts instead of corrected counts is a common error.

What happens to the proton number in beta decay? In beta emission the nucleus gives out an electron (⁰₋₁e), so the proton number Z rises by one while the nucleon number A stays the same. Check that both totals balance in the decay equation.

How is a nuclide written in nuclide notation? The nucleon (mass) number A goes on top and the proton number Z goes underneath, both to the left of the element symbol. Writing them the wrong way round loses the mark.

What must happen before a uranium nucleus undergoes fission? The nucleus must first absorb a neutron. It then splits into two smaller nuclei and releases further neutrons, which can cause a chain reaction.

Official syllabus

Cambridge O Level Physics 5054 syllabus for examination in 2026, 2027 and 2028, Cambridge University Press & Assessment. Section 5, Nuclear physics.