CSEC PHYSICS · SECTION E · LESSON E4

Random Decay, Half-Life and the Uses of Radioisotopes

Why radioactive decay is random, the meaning of half-life, interpreting decay curves, solving half-life problems, and applications such as tracers, medical treatment and carbon dating.

The Physics of the AtomE 3.7E 3.8E 3.9E 3.10E 3.11≈ 50 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON E4 · EXPLAINER

Random Decay, Half-Life and the Uses of Radioisotopes

Radon gas in a basement and carbon dating of an ancient bone both rely on half-life: how long it takes for half of a radioactive sample to decay.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Random decay

Unpredictable for a single nucleus; predictable for large numbers.

Independent of conditions

Not affected by temperature, pressure or chemical state.

Half-life

Time for half the nuclei to decay (or the count rate to halve).

Constant

The same for any amount of the isotope.

Fraction left

(½)ⁿ with n = t ÷ T½.

Decay graph

Exponential: use more than one pair of values.

Uses

Tracers, radiotherapy, sterilising, smoke alarms, thickness gauges, carbon dating.

Carbon dating

C-14 half-life 5 730 years.

EXAM TIPS & COMMON MISTAKES

  • Write the number of half-lives first, then halve the quantity that many times.
  • On a graph show your working: horizontal and vertical lines to the curve.
  • For “one-sixteenth” remember 4 half-lives: ½ → ¼ → ⅛ → 1/16.
  • January 2026 candidates found the half-life graph question hard (mean 1.42 out of 7): practise reading half-life and the time to reach 1/16.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Physics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Syllabus E 3.7

1. Radioactive decay is described as random because

Answer: A. Only the average behaviour is predictable.
Syllabus E 3.8

2. Which of the following can change the half-life of a radioactive isotope?

Answer: D. Decay is independent of external conditions.
Syllabus E 3.9

3. The half-life of a radioactive substance is the time for

Answer: B. That is the definition.
Syllabus E 3.10

4. A sample has a half-life of 4 days. The fraction left after 12 days is

Answer: C. 3 half-lives: (½)³ = 1/8.
Syllabus E 3.10

5. A sample of mass 64 g has a half-life of 10 min. The mass left after 30 min is

Answer: D. 64 → 32 → 16 → 8.0 g.
Syllabus E 3.10

6. The count rate falls from 640 to 40 per minute in 20 days. The half-life is

Answer: A. 640 → 320 → 160 → 80 → 40: 4 half-lives = 20 days.
Syllabus E 3.11

7. Carbon dating uses the isotope

Answer: C. C-14 decays with a half-life of 5 730 years.
Syllabus E 3.11

8. A radioisotope used as a medical tracer should have

Answer: B. It should leave the body quickly and be detectable outside.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (15 marks in total). Show all your working — method marks count. Your answers are saved on this device.

Paper 2 style · Half-life (graph question)

Question 1 [15 marks]

The mass of a radioactive isotope in a sample is 80 g at t = 0 and falls to 40 g after 6.0 days.

(a) (a) Define half-life. [2]

MARK SCHEME — (a) (max 2)

(b) (b) State the half-life of the isotope. [1]

MARK SCHEME — (b) (max 1)

(c) (c) Calculate the mass of the isotope remaining after 24 days. [3]

MARK SCHEME — (c) (max 3)

(d) (d) Determine the time taken for the mass to fall to one-sixteenth of its original value. [3]

MARK SCHEME — (d) (max 3)

(e) (e) State whether heating the sample would change its half-life, with a reason. [2]

MARK SCHEME — (e) (max 2)

(f) (f) State two uses of radioisotopes. [2]

MARK SCHEME — (f) (max 2)

(g) (g) State how a smaller sample would change the activity readings. [2]

MARK SCHEME — (g) (max 2)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.