Calculating Radioactive Decay (AQA GCSE Physics: Combined Science)

• 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

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