Determining Half-Life (WJEC GCSE Physics: Combined Science)

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

1. Put the sample of 'atoms' into the plastic tub and shake gently to mix them up
2. Throw the 'atoms' into the tray
3. Record the number of decayed 'atoms' and remove them from the sample 
4. Put the undecayed 'atoms' back into the plastic tub
5. 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