Calculating Radioactive Decay (AQA GCSE Physics): Revision Note

Calculating Radioactive Decay

Higher Tier Only

• Half-life is the time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half

• With each half-life, the activity of a sample decreases by half

• The ratio of remaining radioactive nuclei to the decayed 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