Half-Life (Edexcel IGCSE Physics)

Spec point — 7.12 · know the definition of the term half-life and understand that it is different for different radioactive isotopes

Half life

• It is impossible to know when a particular unstable nucleus will decay

• It is possible to find out the rate at which the activity of a sample decreases

  • 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

Measuring half life

• To determine 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

Calculating half-life

Spec point — 7.13 · use the concept of the half-life to carry out simple calculations on activity, including graphical methods

Half life calculations

• 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

A graph can be used to make half-life calculations

The graph 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

• The following table shows that as the number of half-life increases, the proportion of the isotope remaining halves

Half life calculation table

Worked Example The activity of a particular radioactive sample is 880 Bq. After a year, the activity has dropped to 220 Bq.

What is the half-life of this material?

Answer:

Step 1: Calculate how many times the activity has halved

• Initially, the activity was 880 Bq
• After 1 half-life the activity would be 440 Bq
• After 2 half-lives, the activity would be 220 Bq
• Therefore, 2 half-lives have passed

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

880 → from 6 months to 1 half life of 440 → from 1 year to 2 half lives of 220

• So two half-lives is 1 year, and one half-life is 6 months
• Therefore, the half-life of the sample is 6 months

Worked Example The radioisotope technetium is used extensively in medicine. The graph below shows how the activity of a sample varies with time.

Determine the half-life of this material.

Answer:

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
• Therefore, the half-life of this isotope is 6 hours