Half-life (AQA GCSE Physics Combined Science): Revision Notes
Half-life
What is half-life?
Half-life is the time it takes for half of the unstable atoms in a radioactive sample to decay. Think of it like this - if you start with 100 unstable atoms, after one half-life you'll have 50 left. After another half-life, you'll have 25 left, and so on.
The activity of a radioactive source tells us how many atoms are decaying each second. This is measured in Becquerels (Bq). As time passes, the activity gets smaller because there are fewer unstable atoms left to decay.
The concept of half-life applies to any radioactive material, regardless of whether it's a naturally occurring element or artificially created in a laboratory. Each radioactive isotope has its own unique half-life, ranging from fractions of a second to billions of years.
Understanding unstable atoms
Some atoms have nuclei that are unstable. These atoms will eventually break apart in a process called radioactive decay.
Here's what happens:
- As more atoms decay, fewer unstable ones remain
- This means the activity of the sample decreases over time
- We can't predict exactly when one particular atom will decay
- But we can predict how many will decay in a given time period
Key Insight: While we cannot predict when any individual atom will decay, the behaviour of large numbers of atoms follows very predictable statistical patterns. This is what makes half-life calculations so reliable and useful.
The half-life pattern
The key thing about half-life is that it follows a predictable pattern. No matter what the starting amount is, the same fraction will always decay in each half-life period.
The Half-Life Pattern:
- After 1 half-life: 50% of the original radioactive atoms remain
- After 2 half-lives: 25% of the original atoms remain
- After 3 half-lives: 12.5% of the original atoms remain
- After 4 half-lives: 6.25% of the original atoms remain
This pattern continues indefinitely, with the amount halving each time.
Half-life calculations
Understanding the mathematics behind half-life helps you solve problems involving radioactive decay.
Worked Example: Calculating Activity Over Time
A radioactive source starts with an activity of 240 Bq and has a half-life of 6 hours.
Step 1: After 6 hours (1 half-life) Activity =
Step 2: After 12 hours (2 half-lives)
Activity =
Step 3: After 18 hours (3 half-lives) Activity =
Step 4: After 24 hours (4 half-lives) Activity =
Notice how each calculation simply divides the previous result by 2. You can also use the formula: Final Activity = Initial Activity × (1/2)^n, where n is the number of half-lives that have passed.
Reading half-life graphs
When you see a graph of radioactive decay, you'll notice several characteristic features:
- The y-axis shows activity (in Bq)
- The x-axis shows time
- The line curves downward - this is called an exponential decay curve
- The curve gets less steep over time because there are fewer atoms left to decay
To find the half-life from a graph:
- Pick a starting activity value
- Find where the activity has halved
- Read the time difference - this is the half-life
For example, if activity drops from 1000 Bq to 500 Bq in 8 hours, the half-life is 8 hours.
Graph Reading Tip: You can verify your half-life reading by checking if the same time period produces halving at different points on the curve. The half-life should be constant regardless of where you measure it on the graph.
Summary
Key Points to Remember:
- Half-life is the time for half the unstable atoms to decay
- Activity decreases over time as atoms decay
- The pattern is always the same: after each half-life, half the remaining atoms decay
- You can't predict when individual atoms will decay, but you can predict the overall pattern
- Graphs of radioactive decay show a curved line that gets less steep over time
- Each radioactive isotope has its own unique half-life value