Radioactive Decay and Half-life

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CognitoHalf-life and radioactive decay

CognitoUses and hazards of radiation

Key facts & equations

Radioactive decay

Radioactive decay is random and spontaneous — cannot be controlled or predicted for individual nuclei.
Unstable nuclei decay to become more stable.
Activity: number of decays per second. Unit: Becquerel (Bq). 1 Bq = 1 decay per second.
Activity decreases over time as fewer unstable nuclei remain.
Count rate: measured by Geiger-Muller tube (counts per second or per minute).

Half-life

Half-life: the time for half the radioactive nuclei in a sample to decay.
Also: time for activity to halve. Or: time for count rate to halve.
After 1 half-life: 50% remains. After 2: 25%. After 3: 12.5%. After n: (½)ⁿ × original.
Half-life ranges: radon-220 = 55 s. Carbon-14 = 5730 years. Uranium-238 = 4.5 billion years.
From graph: read off time for activity to halve. Repeat to confirm consistency.

Uses of radioactive sources

Medical tracer: gamma source (e.g. Tc-99m), short half-life. Injected/swallowed. Detected outside body. Shows organ function.
Cancer treatment (radiotherapy): gamma radiation focused on tumour. Kills cancer cells.
Sterilisation: gamma radiation kills bacteria on medical equipment.
Smoke detectors: americium-241 (alpha). Ionises air between plates → current flows. Smoke blocks alpha → current drops → alarm.
Carbon dating: carbon-14 (beta). Ratio of C-14 to C-12 gives age of organic material.

Hazards and precautions

Ionising radiation damages cells and DNA — can cause mutations and cancer.
Alpha most dangerous inside body. Gamma most dangerous outside body.
Precautions: lead shielding, thick concrete walls, robotic handling, minimum exposure time, maximum distance.
Background radiation: cosmic rays, radon gas, medical sources, food, rocks.
Background must be subtracted from readings to find true source activity.

Exam questions — 4 questions · 10 marks · AQA 8463 style

3 marksHalf-life calculationAQA 8463 P2 style 🔢 Calculator

A radioactive source has initial activity of 800 Bq. Its half-life is 4 hours. Calculate the activity after 12 hours. (3 marks)

Hint: Step 1: how many half-lives in 12 hours? Step 2: halve the activity once for each half-life.

+30 XP

1 markHalf-life definitionAQA 8463 style

Which statement correctly defines half-life?

A The time for all radioactive nuclei to decay

B The time for half of the radioactive nuclei to decay (or for activity to halve)

C The time for the activity to fall to zero

D The time for one nucleus to decay

1 markSmoke detectorAQA 8463 style

Why is an alpha source used in smoke detectors rather than a gamma source?

A Alpha radiation is cheaper to produce

B Alpha particles ionise the air between the electrodes, creating a current; they cannot penetrate the casing and pose no external hazard

C Gamma radiation would not detect smoke particles

D Alpha radiation has a longer range in air than gamma

4 marksMedical tracer requirementsAQA 8463 style

A radioactive tracer is to be used to investigate kidney function. State two properties the tracer must have and explain why each property is important. (4 marks)

Hint: Two properties + reasons. Think: how does the radiation get OUT of the body (must be gamma)? How do we protect the patient (short half-life)?

+40 XP

Radioactive Decay and Half-life

Radioactive decay

Half-life

Uses of radioactive sources

Hazards and precautions

Module complete! 🎉