IGCSE 0625 / Section 5.2.4 / Core

Halving, and halving again.

You cannot say when one nucleus will decay, but you can say exactly how long it takes for half of a whole sample to go. That steady halving, the same for a given isotope every time, is the half-life.

The key idea

The half-life is the time for half the radioactive nuclei in a sample to decay, which is the same as the time for the activity to fall to half. Decay is random, but each isotope has a fixed half-life.

Definition · learn the exact words

The half-life of a radioactive isotope is the time taken for half the radioactive nuclei in a sample to decay, or for the activity (count rate) to fall to half.

each half-life halves what remains

Radioactive decay is random, but the half-life is constant for a given isotope.

Section 01

Count down by halves.

Watch the activity fall to a half, then a quarter, then an eighth, one half-life at a time.

Stage 1 · Learn

Check half life

Four quick checks. Each correct answer earns XP and lights this skill on your star map.

Quick check+10 XP

The half-life is the time for...

Quick check+10 XP

After one half-life, the activity of a source is...

Quick check+10 XP

After two half-lives, the fraction of the original nuclei remaining is...

Quick check+10 XP

Radioactive decay of individual nuclei is...

Section 02

Fractions after each half-life.

One half-life leaves a half, two leave a quarter, three leave an eighth.

Worked example

A source has an activity of 800 Bq and a half-life of 6 hours. Find its activity after 18 hours.

Step 1 · Number of half-lives18 ÷ 6 = 3 half-lives
Step 2 · Halve three times800 → 400 → 200 → 100
Step 3 · Answer100 Bq
Examiner trap

Each half-life halves what is left, it does not subtract a fixed amount. After two half-lives a quarter remains, after three an eighth, never reaching zero in a fixed number of steps. Decay is random but the half-life is constant.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 2.

Finish the four checks above to unlock the exam questions
Exam style+20 XP

A source has an activity of 800 Bq and a half-life of 6 hours. After 18 hours its activity is...

Exam style+20 XP

After 3 half-lives, the fraction of the original radioactive nuclei remaining is...

Exam style+20 XP

The activity of a source falls from 240 Bq to 30 Bq. This took...

Skill unlocked

Half life, mastered.

Half-life is mapped. Keep the chain going.

-Rank -Level -Score -Topics
Go deeper · practice
Six original Cambridge-style questions
The half-life and simple calculations of activity and fraction remaining after whole numbers of half-lives. Attempt each, then reveal the worked solution.
Stage 3 · master the unit
Nuclear physics challenge
Mixed questions across the whole unit, each one worth XP. Start this only when you feel confident across every topic in the unit, not just half life.
Start the unit challenge →