Core · Practice questions · Half-life

Halve, and halve again.

Six original Cambridge-style questions on half-life: the definition, halving calculations, reading a half-life from data, and choosing a source.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

What the examiner wants

Count the half-lives, then halve.

Half-life: time for the activity (or undecayed nuclei) to fall to half.
After n half-lives: fraction left = one over two to the power n.
Time: number of half-lives multiplied by the half-life.

Recall

[1 mark]

Define the half-life of a radioactive source.

The time taken for half the undecayed nuclei (or for the activity) to fall to half. ✓

Calculation

[2 marks]

A source has an activity of 480 counts per second. Its half-life is 2 hours. What is the activity after 6 hours?

half-lives = 6 / 2 = 3 ; halve three times: 480 to 240 to 120 to 60

activity after 6 hours = 60 counts per second

Calculation

[2 marks]

A sample contains 8000 undecayed nuclei. The half-life is 5 days. How many remain undecayed after 15 days?

half-lives = 15 / 5 = 3 ; 8000 to 4000 to 2000 to 1000

1000 nuclei remain undecayed

Calculation

[3 marks]

The activity of a source falls from 1600 counts per second to 200 counts per second in 24 minutes. Calculate the half-life.

1600 to 800 to 400 to 200 is 3 halvings half-life = 24 / 3 = 8

half-life = 8 minutes

Analysis

[2 marks]

A student says that after two half-lives a radioactive source has completely decayed. Explain why this is wrong, and state how much is actually left.

Each half-life removes half of what is left, not half of the original each time. ✓
After two half-lives a quarter is still left. ✓

Application

[2 marks]

A radioactive tracer is to be injected into a patient. Explain why a source with a short half-life of a few hours is more suitable than one with a half-life of many years.

A short half-life means the source decays away quickly. ✓
So the patient is not exposed to radiation for a long time. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.