Half-Life (Edexcel IGCSE Physics (Modular))

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

• 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