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CognitoHalf-life calculations and graphs
Key facts & equations
Reading half-life from a graph
- Plot count rate (or activity) vs time.
- Find the starting activity. Halve it. Read off the time for activity to reach that value.
- Repeat: halve again, read off time. The time interval should be consistent (= half-life).
- Subtract background radiation from all readings before plotting.
- Background count: measure before experiment. Subtract from all readings.
Background radiation subtraction
- Background radiation is always present (cosmic rays, radon, rocks, food, medical).
- Background must be subtracted to find the true count rate from the source alone.
- Net count rate = measured count rate − background count rate.
- If background = 30 cpm and measured = 330 cpm → net = 300 cpm.
- Background stays constant; source count rate decreases with time.
Common mistakes in half-life questions
- Not subtracting background radiation before calculating half-life.
- Using count rate instead of net count rate.
- Not reading the graph carefully at the correct activity levels.
- Confusion between half-life (time for activity to halve) and time to reach zero (impossible).
- AQA exam: always state your starting count rate and halved value explicitly.
Exam questions — 4 questions · 11 marks · AQA 8463 style
⚡ Show all working — the AI marks against the AQA mark scheme. Method marks awarded for correct working even if the final answer is wrong.
4 marksHalf-life from dataAQA 8463 P2 style 🔢 Calculator
A Geiger counter gives the following readings: t=0: 840 cpm; t=10 min: 440 cpm; t=20 min: 240 cpm; t=30 min: 140 cpm. Background = 40 cpm. (a) Calculate net count rate at t=0. (b) Determine the half-life. (3 marks)
Hint: Always subtract background first. Then look for when net count halves — that time interval is the half-life.
+40 XP
1 markBackground radiation sourceAQA 8463 style
Which of the following is NOT a source of background radiation?
A Cosmic rays from space
B Radon gas in buildings
C Mobile phone signals
D Medical X-rays and nuclear medicine
4 marksHalf-life graph descriptionAQA 8463 style
Describe the shape of a graph of count rate vs time for a radioactive source, and explain why the count rate never reaches zero. (3 marks)
Hint: Describe: steep at first, flattening curve (exponential). Why not zero: decay is random so some nuclei always remain; background always present.
+40 XP
Module complete! 🎉
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