Radioactivity — OCR A Level Physics
Module 5 · Nuclear and Particle Physics

Radioactivity

Specification: OCR A H556  |  Section: 5.4.2  |  Teaching time: ~4 hours

By the end of this topic you should be able to…
Part 1

Types of Nuclear Radiation

Radioactivity is the spontaneous emission of particles or energy from an unstable nucleus. The nucleus becomes more stable by losing energy through radioactive decay. This process is random and unaffected by external conditions (temperature, pressure, chemical bonding).

There are four main types of nuclear radiation you need to know:

Type Symbol Composition Charge Mass (u) Penetrating power
Alpha α Helium nucleus (2p + 2n) +2e 4 Stopped by paper, ~5 cm air
Beta-minus β⁻ Electron (from neutron decay) −e 1/1836 ≈ 0 Stopped by ~3 mm aluminium
Beta-plus β⁺ Positron (from proton decay) +e 1/1836 ≈ 0 Annihilates with electrons
Gamma γ EM photon (high energy) 0 0 Reduced by lead, not stopped
⚠️ Common Misconception

Alpha particles are the most ionising but least penetrating. Gamma rays are the least ionising but most penetrating. Ionising ability and penetrating power are inversely related.

Ionisation occurs when radiation removes electrons from atoms, creating ions. The greater the charge and mass of the particle, the more ionising it is. Ionisation damages cells by breaking chemical bonds and damaging DNA.

Part 2

Nuclear Equations

All nuclear equations must conserve mass number (A = nucleons) and atomic number (Z = protons).

Alpha decay: The nucleus emits an α particle (helium nucleus).

General alpha decay AZX → A−4Z−2Y + 42α

Example: Radium-226 decays by alpha emission:

Radium decay 22688Ra → 22286Rn + 42α

Beta-minus decay: A neutron converts to a proton, emitting an electron and antineutrino.

Beta-minus decay n → p + e⁻ + v̄e

Example: Carbon-14 decays by beta-minus emission:

Carbon-14 decay 146C → 147N + 0−1e + v̄e

Beta-plus decay: A proton converts to a neutron, emitting a positron and neutrino.

Beta-plus decay p → n + e⁺ + ve

Gamma emission: The nucleus loses energy by emitting a gamma photon. Mass number and atomic number do not change.

⚡ Exam Tip

In nuclear equations, always check that the top numbers (mass) and bottom numbers (atomic/proton) balance on both sides. For β⁻, the electron is written as 0−1e (mass 0, charge −1).

Check your understanding

Knowledge Check

1
Uranium-238 decays by alpha emission. Write the nuclear equation and identify the daughter nucleus.
3 marks

23892U → 23490Th + 42α (2 marks for correct equation)

Daughter nucleus: Thorium-234 (Th-234) (1 mark)

2
Explain why alpha particles are more ionising than gamma rays of the same energy.
2 marks
  • Alpha particles have +2 charge and greater mass (1 mark)
  • They interact more strongly with electrons, removing them from atoms more effectively (1 mark)
Part 3

Radioactive Decay and Half-Life

Activity (A) is the rate at which a source decays, measured in becquerels (Bq), where 1 Bq = 1 decay per second.

Half-life (T½) is the time taken for half the unstable nuclei in a sample to decay, or for the activity to halve.

Radioactive decay follows an exponential pattern:

Exponential decay N = N0e−λt     A = A0e−λt

Where λ is the decay constant (probability of decay per nucleus per second).

Half-life relationship T½ = ln(2) / λ ≈ 0.693 / λ

The number of undecayed nuclei after n half-lives is:

Multiple half-lives N = N0 × (½)n   where n = t / T½
⚡ Key Point

Half-life is constant for a given isotope, regardless of the starting amount. After 1 half-life, 50% remains. After 2 half-lives, 25% remains. After 3 half-lives, 12.5% remains.

Interactive

Radioactive Decay Simulation

Exponential Decay Simulation
Time: 0.0 s
Half-lives: 0.00
Remaining: 100%
Part 4

Background Radiation and Safety

Background radiation is the low-level ionising radiation present everywhere. Sources include:

  • Radon gas (~50%) — from rocks and soil
  • Medical (~14%) — X-rays, radiotherapy
  • Ground and buildings (~14%) — rocks, building materials
  • Cosmic rays (~10%) — high-energy particles from space
  • Food and drink (~10%) — potassium-40 in bananas, etc.
  • Nuclear industry (~1%) — weapons testing, power stations

Safe handling of radioactive sources:

  • Keep sources in lead-lined containers
  • Use tongs and keep at arm's length
  • Minimise exposure time
  • Maximise distance from source (inverse square law)
  • Use shielding appropriate to radiation type
⚠️ Safety Note

Always measure and subtract background count rate before calculating activity. Typical background: 15–40 counts per minute depending on location.

Exam Practice

Exam-Style Questions

1
Iodine-131 has a half-life of 8.0 days. A sample has an initial activity of 640 Bq.

(a) Calculate the decay constant λ. (2 marks)
(b) Calculate the activity after 24 days. (2 marks)
(c) State why the activity never reaches zero. (1 mark)
5 marks

(a) λ = ln(2) / T½ = 0.693 / (8 × 24 × 3600) = 1.00 × 10−6 s−1 (2 marks)

(b) After 24 days = 3 half-lives. A = 640 × (½)³ = 640 × 0.125 = 80 Bq (2 marks)

(c) Exponential decay approaches zero asymptotically / there will always be some undecayed nuclei remaining (1 mark)

2
A radioactive source emits both alpha and gamma radiation.

(a) Describe how you would demonstrate that the source emits both types of radiation. (3 marks)
(b) Explain which type of radiation would be most dangerous if the source were: (i) ingested, (ii) held 1 m from the body. (4 marks)
7 marks

(a) Use a Geiger-Müller tube to measure count rate. Place paper in front of source — count should drop (alpha blocked). Then place aluminium sheet — count should drop further (any beta blocked). Remaining count is from gamma (passes through). (3 marks)

(b) (i) Alpha is most dangerous if ingested because it is highly ionising and can damage cells directly. Gamma would pass through with minimal interaction. (2 marks)

(ii) Gamma is most dangerous at 1 m because alpha is stopped by air (~5 cm). Gamma has high penetrating power. (2 marks)

Topic Summary

Radiation types

α (He nucleus), β⁻ (electron), β⁺ (positron), γ (photon) — differ in charge, mass, penetration, ionisation

Half-life

T½ = 0.693/λ, constant for each isotope, exponential decay

Activity

A = λN measured in Bq (decays per second), A = A₀e−λt

Equations to Know
N = N₀e−λt
T½ = ln(2)/λ
A = λN
A = A₀e−λt
N = N₀(½)n