Modelling Radioactive Decay
- It cannot be predicted when a particular unstable nucleus will decay
- This is because radioactive decay is a random process, this means that:
- There is an equal probability of any nucleus decaying
- It cannot be known which particular nucleus will decay next
- It cannot be known at what time a particular nucleus will decay
- The rate of decay is unaffected by the surrounding conditions
- It is only possible to estimate the probability of nuclei decaying in a given time period
- For example, a researcher might take some readings of background radiation
- If they were to reset the counter to zero, wait one minute and then take the readings again, they might obtain a set of results such as:
32 11 25 16 28
- The readings don't appear to follow a particular trend
- This happens because of the randomness of radioactive decay
- The random nature of radioactive decay can be demonstrated by observing count rate with a Geiger-Muller (GM) tube
- When a GM tube is placed near a radioactive source, the counts are found to be irregular and cannot be predicted
- Each count represents a decay of an unstable nucleus
- These fluctuations in count rate on the GM tube provide evidence for the randomness of radioactive decay
Count Rate for a Radioactive Substance
The variation of count rate with time of a radioactive substance. The fluctuations show the randomness of radioactive decay
Modelling Radioactive Decay
- A model, or analogy, is a way of understanding an idea by using a different but similar situation
- Radioactive decay can be modelled using
- A large collection of dice or coins
- A computer simulation or spreadsheet programme
- Rolling dice is a good analogy for radioactive decay because it is also a random process
Dice represent the random nature of radioactive decay
A dice roll is a random process because you don't know when you will roll a particular value. However, you can determine the probability of a particular result
- Imagine rolling a dice and hoping to roll a '6'
- 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 '6'
- If you rolled the dice 1000 times, you can expect to roll a '6' around 1000 ÷ 6 ≈ 127 times
Exam Tip
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 as with rolling a die, 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.
