Calculating Radioactive Decay (AQA GCSE Physics)

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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

    • The time period is 15 years
    • The half-life is 3 years

15 ÷ 3 = 5

    • There have been 5 half-lives

Step 2: Raise 1/2 to the number of half-lives

(1/2)5 = 1/32

    • So 1/32 of the original nuclei are remaining

Step 3: Write the ratio correctly

    • 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

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Ashika

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