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Year 11
AQA
Higher

Activity and half-life calculations (including complex ones)

I can interpret radioactive half-life graphs and make calculations using values of half-life.

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Share activities with pupils
New
New
Year 11
AQA
Higher

Activity and half-life calculations (including complex ones)

I can interpret radioactive half-life graphs and make calculations using values of half-life.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The amount (or activity) of a radioactive isotope repeatedly falls by half in equal amounts of time.
  2. A radioactive half-life graph shows the amount (or activity) of a radioactive isotope plotted against time.
  3. In 2 half-lives the amount (or activity) of a radioactive isotope falls to ½ × ½ = ¼ as much.
  4. In 3 half-lives the amount (or activity) of a radioactive isotope falls to ½ × ½ × ½ = 1/8 as much, and so on.
  5. Radioactive isotopes with short half-lives decay quickly, emitting most radiation over a short period of time.

Common misconception

It is impossible to predict outcomes for random events such as radioactive decay.

Use analogies to show that random nuclear decay can lead to predictable outcomes, such as the randomness in the order popcorn kernels pop, but the predictability of how quickly all the popcorn takes to cook.

Keywords

  • Activity - the number of decays per second; it is measured in becquerels (Bq)

  • Radioactive isotopes - contain unstable nuclei that will decay over time and emit ionising radiation

  • Radioactive half-life - the time taken for the activity of a sample of a radioactive isotope to halve

Use exam questions to provide lots of practice of half-life calculations in a range of different contexts.
Teacher tip

Content guidance

  • Depiction or discussion of sensitive content

Supervision

Adult supervision recommended

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Which of the following describes what is meant by a radioactive isotope having a half–life of 15 minutes?
It takes 30 minutes for all of the nuclei to decay.
It takes 15 minutes for one nucleus to decay.
Correct answer: It takes 15 minutes for half of the nuclei to decay.
Q2.
How do the half–lives of different radioactive isotopes compare?
All radioactive isotopes have the same half–life.
Isotopes of the same element have the same half–life.
Correct answer: Half–life values vary between different isotopes and elements.
Half–life does not depend on the radioactive isotope.
Q3.
What effect does increasing the temperature have on the half–life of a radioactive isotope?
Increasing the temperature increases the half–life.
Increasing the temperature decreases the half–life.
Correct answer: Increasing the temperature has no effect on the half–life.
Q4.
Starting with the longest, sort the following radioactive isotopes into order of decreasing half–life.
1 - plutonium–239: half–life = 24,100 years
2 - americium–241: half–life = 432 years
3 - hydrogen–3 (tritium): half–life = 12.3 years
4 - iodine–131: half–life = 8 days
5 - polonium–214: half–life = 0.16 milliseconds
Q5.
How does the half–life of a carbon–14 atom in a carbon monoxide (CO) molecule compare to its half–life in a carbon dioxide (CO₂) molecule?
It is longer when part of the CO molecule.
It is longer when part of the CO₂ molecule.
Correct answer: It is the same, regardless of the molecule it is part of.
Q6.
A radioactive isotope has a half–life of 10 hours. Match each of the following fractions of the sample remaining to the correct amount of time that has passed.
Correct Answer:1,0 hours

0 hours

Correct Answer:½,10 hours

10 hours

Correct Answer:¼,20 hours

20 hours

Correct Answer:⅛,30 hours

30 hours

Exit quiz

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6 Questions

Q1.
The activity of a sample of a radioactive isotope is …
Correct answer: measured in becquerels (Bq).
Correct answer: the number of decays per second.
the total mass of the sample.
Correct answer: the rate at which the sample emits radiation.
the number of nuclei in the sample.
Q2.
An activity of 100 becquerel (Bq) means …
1 nucleus decays every 100 seconds.
Correct answer: 100 nuclei decay every second.
there are 100 radioactive nuclei in a sample.
100 nuclei decay after each half–life has passed.
Q3.
Which of the following can be used to define what is meant by the half–life of a radioactive isotope?
Correct answer: The time it takes for its activity to fall to half of its initial value.
Half the time it takes for its activity to fall to zero.
Correct answer: The time it takes for half of the nuclei to decay.
Half the time it takes for all of the nuclei to decay.
The time it takes for half of a nucleus to decay.
Q4.
Sodium–24 has a half–life of 15 hours. If a sample of sodium–24 originally has an activity of 500 Bq, what fraction of its original activity will remain after 30 hours?
½
Correct answer: ¼
⅛
0
Q5.
After 42 days the activity of a sample of phosphorus–32 has decreased from 400 Bq to 50 Bq. What is the half–life of phosphorus–32?
7 days
Correct answer: 14 days
126 days
168 days
Q6.
The half–life of protactinium–234 is 6.75 hours. What percentage of the original sample will have decayed after 13.5 hours?
100%
Correct answer: 75%
50%
5%