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5.2.3 Radioactive Decay

Nuclear physics · IGCSE Physics

5.2.3 Radioactive Decay — IGCSE Physics Notes

Exam years: 2025–2027 Topic: Nuclear physics Lesson 42 of 48

5.2.3 Radioactive Decay

Definition of Radioactivity

Radioactivity is a change in an unstable nucleus that can result in the emission of α (alpha) particles, β⁻ (beta) particles, and/or γ (gamma) radiation.

Key Characteristics

  • Radioactive changes are spontaneous and random — they cannot be predicted or controlled.
  • Isotopes may be radioactive due to:
    • Excess neutrons in the nucleus, or
    • A nucleus too heavy to remain stable.
  • During α-decay or β-decay, the nucleus transforms into that of a different element.
  • Decay increases nuclear stability by reducing excess neutrons and energy.

Change During Beta Emission

In β⁻ decay, a neutron changes into a proton and an electron.

neutron → proton + electron

Products of Nuclear Decay

A radioactive substance emits one or more of the following radiations during decay, often accompanied by the release of energy.

Alpha Decay (α)

  • The nucleus loses two protons and two neutrons (an alpha particle).
  • Mass number decreases by 4; atomic number decreases by 2.
  • A new element is formed that is two places lower in the Periodic Table.

Example:

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

  • Uranium-238 decays into thorium-234 and emits an alpha particle.

Beta Decay (β⁻)

  • A neutron changes into a proton and emits an electron (beta particle).
  • Mass number remains the same; atomic number increases by 1.
  • The nucleus of the new atom has one more proton and one less neutron.

Example:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

  • Carbon-14 decays into nitrogen-14 and emits a beta particle.

Gamma Decay (γ)

  • Occurs after α or β decay, when the nucleus remains in an excited state with extra energy.
  • The nucleus emits a gamma ray — a wave of high-frequency electromagnetic radiation.
  • No change in atomic number or mass number.
  • Gamma emission helps the nucleus lose excess energy and become more stable.

Example:

⁶⁰₂₇Co* → ⁶⁰₂₇Co + γ

  • The excited nucleus of cobalt-60 emits a gamma ray and returns to a stable energy state.

Summary of Decay Effects

5.2.4 Half-Life

Definition

Half-life is defined as the time taken for:

  • The number of nuclei of a radioactive isotope in a sample to fall to half its original value, or
  • The count rate or activity to drop to half its initial value, or
  • The mass of a radioactive isotope to decrease to half its original mass.

Understanding Decay and Half-Life

  • Radioactive decay is random and spontaneous.
  • The half-life for a particular isotope is constant and unaffected by temperature, pressure, or chemical changes.
  • Each half-life, half of the remaining nuclei decay — so the amount of activity decreases exponentially.

Examples and Applications

  • Example: A 400 mg sample with a half-life of 5 days will reduce to 100 mg after 10 days.
  • If the half-life is 70 s, after one half-life the count rate falls to half its initial value.
  • Decay curves can be plotted showing how activity or count rate decreases over time.

Determining Half-Life from a Graph

  • Subtract background radiation from all measured count rates.
  • Plot the corrected count rate against time.
  • Find the time taken for the count rate to drop to half its initial corrected value.
  • This time interval is the half-life.

Worked Example

Given: Half-life = 5 days, initial mass = 400 mg.

After 10 days:

  • After 1st half-life (5 days): 200 mg remains.
  • After 2nd half-life (10 days): 100 mg remains.

Answer: 100 mg of radioactive material remains.

Applications of Radioactive Isotopes

Type of DecayChange in Mass NumberChange in Atomic NumberEffect
Alpha (α) −4 −2 New element formed, two places lower in Periodic Table
Beta (β⁻) 0 +1 New element formed, one place higher in Periodic Table
Gamma (γ) 0 0 Nucleus loses excess energy; no change in composition
ApplicationType of RadiationPurpose
Smoke alarms Alpha (α) Detect smoke particles that interrupt the ionisation current.
Sterilising medical instruments Gamma (γ) Kill bacteria and microorganisms on equipment.
Food irradiation Gamma (γ) Kill bacteria and extend shelf life of food products.
Thickness control Beta (β) Used to maintain uniform thickness in paper or metal sheets.
Cancer treatment (radiotherapy) Gamma (γ) Kill cancer cells by focused radiation without surgery.
Cancer diagnosis Gamma (γ) Use radioactive tracers; gamma camera detects emissions from tumour areas.

Explanation — Thickness Monitoring

  • A beta emitter is placed on one side of a sheet and a detector on the opposite side.
  • If the sheet becomes thicker → fewer beta particles pass through → detected activity decreases.
  • This signals the rollers to reduce pressure to maintain correct thickness.
  • Beta radiation is ideal because it can penetrate paper or thin aluminium, but not thick metal.

Explanation — Cancer Treatment and Diagnosis

  • Gamma rays have high penetrating power and can destroy living cells.
  • In radiotherapy, focused gamma beams kill cancer cells without surgery.
  • In diagnosis, radioactive tracers injected into the body emit gamma rays that are detected using a gamma camera.
  • Cancerous cells absorb more tracer due to their higher metabolic rate, forming a brighter image.

Mark Scheme Highlights

  • Always correct for background radiation before analysing decay data.
  • State that half-life is constant and unaffected by external factors.
  • For gamma rays, note they are high-frequency electromagnetic waves with high energy and short wavelength.
  • Lead sheets reduce gamma count rate but do not completely absorb it.
  • Half-life can be determined graphically by finding time for count rate to halve.

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