Half-Life | Physics for Grade 10 PDF Download

Introduction

• It is impossible to know when a particular unstable nucleus will decay
• But the rate at which the activity of a sample decreases can be known
  • This is known as the half-life
• Half-life is defined as:
  • The time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half
• In other words, the time it takes for the activity of a sample to fall to half its original level
• Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length

Using Half-life

• Scientists can measure the half-lives of different isotopes accurately:
• Uranium-235 has a half-life of 704 million years
  • This means it would take 704 million years for the activity of a uranium-235 sample to decrease to half its original amount
• Carbon-14 has a half-life of 5700 years
  • So after 5700 years, there would be 50% of the original amount of carbon-14 remaining
  • After two half-lives, or 11 400 years, there would be just 25% of the carbon-14 remaining
• With each half-life, the amount remaining decreases by half
  
  The diagram shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed
• The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life
• It is the same length of time as it would take to decrease from 50 % activity to 25 % activity
• The half-life is constant for a particular isotope

Calculating Half-Life

• To calculate the half-life of a sample, the procedure is:
  • Measure the initial activity, A0, of the sample
  • Determine the half-life of this original activity
  • Measure how the activity changes with time
• The time taken for the activity to decrease to half its original value is the half-life

Solved Example

Determine the half-life of this material.

Step 1: Draw lines on the graph to determine the time it takes for technetium to drop to half of its original activity

Step 2: Read the half-life from the graph

• In the diagram above the initial activity, A0, is 8 × 10⁷ Bq
• The time taken to decrease to 4 × 10⁷ Bq, or ½ A₀, is 6 hours
• The time taken to decrease to 2 × 10⁷ Bq is 6 more hours
• The time taken to decrease to 1 × 10⁷ Bq is 6 more hours
• Therefore, the half-life of this isotope is 6 hours

Example 2: A particular radioactive sample contains 2 million un-decayed atoms. After a year, there is only 500 000 atoms left un-decayed. What is the half-life of this material?

Step 1: Calculate how many times the number of un-decayed atoms has halved

• There were 2 000 000 atoms to start with
• 1 000 000 atoms would remain after 1 half-life
• 500 000 atoms would remain after 2 half-lives
• Therefore, the sample has undergone 2 half-lives

Step 2: Divide the time period by the number of half-lives

• The time period is a year
• The number of half-lives is 2
• 1 year divided by 2 is half a year or 6 months
• Therefore, the half-life is 6 months