Half-Life (Oxford AQA IGCSE Physics)

Worked Example

The radioisotope technetium is used extensively in medicine. The graph below shows how the count rate 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 count rate

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

Exam Tip

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.