# Simple model of exponential decay

##### Class practical

In this activity, students model radioactive decay using coins and dice. By relating the results from the model to the experimental results in Measuring the half-life of protactinium, students can see that the model helps to explain the way in which a radioactive substance decays. The model provides an insight into what might be happening within radioactive atoms.

This activity is a good analogy of radioactive decay as it is based on probability. The decaying trend will be noticeable and so too will the random nature.

#### Apparatus and materials

Pennies or other coins, plentiful supply

Dice, plentiful supply (OPTIONAL)

#### Health & Safety and Technical notes

The more coins each student has, the better the analogy of radioactive decay. You could use as few as one per student to keep it simple. Any more than four is quite difficult to manage.

Small coins will turn around more in their cupped hands.

A canvas bag containing 500 plastic cubes (each side 10 mm), each with one face identified, is available in the UK from Lascells, order code 60-010.

#### Procedure

a Explain the procedure (as follows) to the class.

b Each student has a number of coins. This could be between one and four. They hold them in their cupped hands.

c On your instruction "shake", the students shake their coins for at least 5 seconds (they should ensure that the coins are moving around inside their cupped hands). On the instruction "stop", they stop shaking and open their hands with one hand flat and facing upwards so that they can see their coins.

d If any coins come down heads, they take them out of their palm and place them on the desk.

e On your instruction "show", they put up a number of fingers corresponding to the number of coins they took out of their palm.

f Record this number on the board.

g They keep the remaining coins in their hands and repeat from step c. If you can arrange it that you take a reading once every minute, then you can record the readings against time. It will then give results very similar to protactinium.

h Analyze the result by plotting a graph.

#### Teaching notes

1 You might want to appoint a counter and a scribe to count the coins and record the results.

2 Take care with how you ask students to signal the numbers. They may be tempted to add their own (rude) gestures.

3 Draw out the similarities with the protactinium experiment. The trend is the same and there is also some randomness. The close match between the results from this model and the results from Measuring the half-life of protactinium show that radioactive atoms have a chance of decaying in any fixed time.

4 Use the activity to explain the downward trend of the decay curve. Only coins that are left can 'decay'. As there are fewer of them each time, fewer will decay.

5 The activity raises the interesting question about how long a radioactive source will last and what happens to the last 'atom'.

6 An alternative to shaking the coins in students' palms is to flick them. But this takes longer.

7 You could repeat the experiment with small dice to give a longer half-life. Combining results (as outlined here) makes for a smoother curve.

This experiment was safety-tested in May 2007