Calculating Radioactive Decay | Physics for Grade 10 PDF Download

Introduction

• 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

Solved Example

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