AQA GCSE Physics

Revision Notes

4.2.9 Calculating Radioactive Decay

Higher Tier Only

Calculating Radioactive Decay

  • 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
  • Divide 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 : original 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 : 32 remaining, or 31:32

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Already a member?
Go to Top