AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
(HT only) Students should be able to calculate the net decline, expressed…
Full specification wording
Half-lives and the random nature of radioactive decay: (HT only) Students should be able to calculate the net decline, expressed as a ratio, in a radioactive emission after a given number of half-lives.
After each half-life, the count rate or activity of a radioactive sample falls to half its previous value.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 5 of 5
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
After each half-life, the count rate or activity of a radioactive sample falls to half its previous value. After n half-lives, the remaining fraction is (1/2)ⁿ. The net decline is expressed as a ratio of the final emission to the original emission, which is 1:2ⁿ. For example, after 3 half-lives, the remaining fraction is (1/2)³ = 1/8. The ratio of final to original emission is therefore 1:8. If the starting count rate is 640 counts per minute, after 3 half-lives it is 640 ÷ 8 = 80 counts per minute. The ratio of 80 to 640 simplifies to 1:8.
What earns the marks
- Identify the number of half-lives, n, from the question or by dividing the total time by the half-life.
- Calculate the remaining fraction after n half-lives using (1/2)ⁿ.
- Calculate the net decline ratio as 1:2ⁿ, representing the final emission compared to the original emission.
- Express the answer as a simplified ratio in the form 1:X (e.g., 1:8 after 3 half-lives).
- Show intermediate values, such as the final count rate, to make the calculation method clear.
Common mistakes and how to put them right
Using n/2 instead of (1/2)ⁿ.
Put it right: The process is repeated halving, so use the power (1/2)ⁿ or multiply by 1/2 for each half-life.
Reversing the ratio to 2ⁿ:1 (e.g., 8:1).
Put it right: AQA mark schemes require the ratio of final to original emission, so it should be written as 1:2ⁿ (e.g., 1:8).
Forgetting to simplify the ratio.
Put it right: If calculating from raw count rates like 80:640, divide both sides by the highest common factor to give 1:8.
Exam tips
- Write down the number of half-lives first, then use powers of 2 to find the ratio quickly.
- Always present the net decline ratio in the format 1:2ⁿ unless specifically instructed otherwise.
Try the lesson
The start of the Half-lives and the random nature of radioactive decay: (HT only) Students should be able to calculate the net decline, expressed as a ratio, in a radioactive emission after a given number of half-lives. lesson, made from checked teaching notes for this specification point.
Have a go first
A radioactive source used in a laboratory has an initial count rate of 6400 counts per minute. After 4 half-lives, what is the net decline in the count rate, expressed as a ratio of the decline to the initial count rate?
Listen
After each half-life, the count rate or activity of a radioactive sample falls to half its previous value. After n half-lives, the remaining fraction is (1/2)ⁿ. The net decline is expressed as a ratio of the final emission to the original emission, which is 1:2ⁿ. For example, after 3 half-lives, the remaining fraction is (1/2)³ = 1/8. The ratio of final to original emission is therefore 1:8. If the starting count rate is 640 counts per minute, after 3 half-lives it is 640 ÷ 8 = 80 counts per minute. The ratio of 80 to 640 simplifies to 1:8. A strong answer earns marks for these points. Identify the number of half-lives, n, from the question or by dividing the total time by the half-life. Calculate the remaining fraction after n half-lives using (1/2)ⁿ. Calculate the net decline ratio as 1:2ⁿ, representing the final emission compared to the original emission. Express the answer as a simplified ratio in the form 1:X (e.g., 1:8 after 3 half-lives). A common slip: Using n/2 instead of (1/2)ⁿ. Instead, the process is repeated halving, so use the power (1/2)ⁿ or multiply by 1/2 for each half-life. Exam tip: Write down the number of half-lives first, then use powers of 2 to find the ratio quickly.
See it
Key words
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net decline
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half-life
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remaining fraction
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See every definition
- net decline
- The fall in a radioactive emission after a given number of half-lives, expressed as a ratio of the final emission to the original emission.
- half-life
- The time after which the count rate or activity of a radioactive sample falls to half its previous value.
- remaining fraction
- The amount left after n half-lives, found using (1/2)ⁿ because the process is repeated halving.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
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