Calculating Radioactive Decay (HT only)
- With each half-life, the activity of a sample decreases by half
- The ratio of remaining radioactive nuclei after a period of time can be calculated in different ways
Method 1: Halving Method
- Determine the number of half-lives elapsed
- Multiply the number 1 by half for each half-life elapsed
- For example, if 4 half-lives have elapsed:
1 × ½ × ½ × ½ × ½ = 1 / 16
- This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16
Method 2: Raising to a Power
- Determine the number of half-lives elapsed
- Use your calculator to raise ½ to the number of half-lives
- For example, if 4 half-lives have elapsed:
(1/2)4 = 1/16
- This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16
Worked example
A radioactive sample has a half-life of 3 years. What is the ratio of decayed : remaining nuclei, after 15 years?
Step 1: Calculate the number of half-lives
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- The time period is 15 years
- The half-life is 3 years
15 ÷ 3 = 5
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- There have been 5 half-lives
Step 2: Raise 1/2 to the number of half-lives
(1/2)5 = 1/32
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- So 1/32 of the original nuclei are remaining
Step 3: Write the ratio correctly
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- If 1/32 of the original nuclei are remaining, then 31/32 must have decayed
- Therefore, the ratio is 31 decayed : 1 remaining, or 31:1
