Determining Half-Life (WJEC GCSE Science (Double Award)): Revision Note
Specified Practical: Determining Half-Life
Aim of the Experiment
The aim of the experiment is to determine the half-life of a sample of dice (or coins) as a simulation of the process of radioactive decay
Variables:
Independent variable = Number of throws
Dependent variable = Number of undecayed 'atoms' (cubes, dice or coins)
Control variables:
Total number of 'atoms' (cubes, dice or coins)
Equipment List
Equipment | Purpose |
|---|---|
A large sample of (at least 50) dice, shaded cubes or coins | To simulate the unstable atoms of a radioactive element |
Plastic tub | To use as a container to throw the sample from |
Tray | To provide a surface for the sample to land on |
Equipment Set Up
Radioactive decay can be modelled using a large sample of cubes
Method
Put the sample of 'atoms' into the plastic tub and shake gently to mix them up
Throw the 'atoms' into the tray
Record the number of decayed 'atoms' and remove them from the sampleĀ
Put the undecayed 'atoms' back into the plastic tub
Repeat the process a total of 10 times
If using cubes with one face shaded to represent the atoms:
The cubes that land with the shaded face upwards represent decayed radioactive atoms
The cubes that land with any of the coloured faces upwards represent undecayed radioactive atoms
If using dice to represent the atoms:
The dice that land a '6' represent decayed radioactive atoms
The dice that land any number 1-5 represent undecayed radioactive atoms
If using coins to represent the atoms:
The coins that land as heads represent decayed radioactive atoms
The coins that land as tails represent undecayed radioactive atoms
An Example Table of Results
An Expected Table of Results
Roll number | Cubes remaining - Group 1 | Cubes remaining - Group 2 | Cubes remaining - Group 3 | Cubes remaining - Group 4 | Cubes remaining - Group 5 | Total cubes remaining |
|---|---|---|---|---|---|---|
0 | 50 | 50 | 50 | 50 | 50 | 250 |
1 | 45 | 42 | 40 | 42 | 38 | 207 |
2 | 36 | 31 | 38 | 36 | 34 | 175 |
3 | 28 | 26 | 30 | 29 | 30 | 143 |
4 | 23 | 18 | 24 | 25 | 26 | 116 |
5 | 20 | 14 | 20 | 22 | 24 | 100 |
6 | 17 | 10 | 16 | 19 | 20 | 82 |
7 | 15 | 7 | 13 | 15 | 17 | 67 |
8 | 14 | 6 | 10 | 12 | 14 | 56 |
9 | 10 | 4 | 9 | 11 | 12 | 46 |
10 | 7 | 2 | 6 | 8 | 9 | 32 |
Analysis of Results
The results can be plotted on a graph
On the y-axis, plot the number of 'atoms' remaining and plot the number of throws on the x-axis
On the curve, draw a horizontal line at half the initial number of 'atoms' remaining and then draw a vertical line down from the curve to find the number of throws this occurs at
This gives the half-life of the model
For one set of results (e.g. 50 cubes), the graph may have the following shape:
Example Graph for Modelling Radioactive Decay
A graph of number of 'atoms' remaining against number of throws can be used to determine the half-life of a sample
When many sets of results are collected (e.g. from several groups in one class), this can be plotted to see the variation when a larger sample is used
The advantages of using a larger sample are
It reduces the effects of anomalous results
It gives a smoother curve which means it is a better representation of radioactive decay
Example Graph for a Larger Sample
Using a larger sample size is likely to produce a better representation of exponential decay
Evaluating the Experiment
Systematic Errors:
To ensure the experiment is fair, each die, cube, or coin must be identical (i.e. not weighted)
Random Errors:
Random errors and anomalous results can be reduced by increasing the sample size i.e. a greater number of groups carrying out the same experiment
Safety Considerations
There are no significant safety considerations in carrying out this experiment
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