Half-Life (Oxford AQA IGCSE Physics)

Revision Note

Caroline Carroll

Written by: Caroline Carroll

Reviewed by: Lucy Kirkham

Half-Life

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

  • With a large enough sample of unstable nuclei, it becomes possible to predict how many unstable nuclei will undergo radioactive decay

  • The half-life of a radioactive isotope is defined as:

The average time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half

  • In other words, half-life is the time it takes for the count rate 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 count rate 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 number of nuclei of the original element remaining decreases by half

  • Remember that when the nuclei decay, they become another element, they do not disappear

  • For this reason, the mass of the sample does not significantly change

Graph of count rate against time

Half-life Graph, for IGCSE & GCSE Physics revision notes
The diagram shows how the count rate of a radioactive sample changes over time. Each time the count rate halves, another half-life has passed
  • The time it takes for the count rate 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 count rate of the sample

    • Measure how the count rate changes with time

  • The time taken for the count rate to decrease to half its original value is the half-life

Worked Example

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

Worked example using a half-life curve. The curve shows that the initial count rate is 800 counts per minute. After 6 hours, the count rate has fallen to 400 counts per minute and after 12 hours, the count rate has fallen to 200 counts per minute

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 count rate

Annotated decay curve showing a line drawn from the point when the activity had halved to the curve, then down to the time axis. The half life is shown to be 6 hours.

Step 2: Read the half-life from the graph

  • In the diagram above the initial count rate is 800 counts per minute

  • The time taken to decrease to 400 counts per minute is 6 hours

  • The time taken to decrease to 200 counts per minute is 6 more hours

  • The time taken to decrease to 100 counts per minute is 6 more hours

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

Worked Example

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?

Answer:

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

Examiner Tips and Tricks

You can use models to demonstrate the random process of radioactive decay.

Imagine rolling a dice and hoping to roll a six. Each time you roll the dice, you cannot know what the result will be, but you know there is a 1/6 probability that it will be a six. If you rolled the dice 1000 times, you can expect to roll a '6' around 1000 ÷ 6 ≈ 127 times

Another common model is to use the flip of a coin to model radioactive decay. For each coin, the probability of a landing 'heads' is 1/2, but we still cannot predict the outcome or confidently say when a 'heads' will appear, this is why it's important to use a very large sample of coins (or dice!) to represent the process of radioactive decay.

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Caroline Carroll

Author: Caroline Carroll

Expertise: Physics Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.

Lucy Kirkham

Author: Lucy Kirkham

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.