## A random process with fixed chance

Teaching Guidance for 14-16

#### How can radioactive decay be both random and based on fixed chance?

**Wrong Track: **How can it be possible for radioactive decay to be random and yet based on fixed chance at the same time? If the process is random you can't predict it and if it has a fixed chance you can!

**Right Lines: ** If you imagine a stockpile

of atoms making up a radioactive source, it is not possible to predict which atomic nucleus will disintegrate next but there is a fixed chance of disintegration, which applies to all of the atoms.

#### Modelling radioactive decay with dice

**Thinking about the learning**

For some students the idea that the process of radioactive decay can be both a random process and one subject to fixed chance may seem strange.

**Thinking about the teaching**

Experience shows that it is really helpful to model radioactive decay by using a simple dice simulation. In one form of the activity, each student in the class is given 20 dice (radioactive atoms) and all students shake and roll their dice together. A six

is taken to indicate the disintegration of an atom and each time a six appears that dice is removed. The remaining stockpile

of radioactive dice, summed after each throw across all students, follows an exponential decay curve. This activity clearly models the random nature of the event (it's not possible to predict which dice will disintegrate next) along with the underlying fixed chance (one in six) of decay.

We'd suggest emphasising that it's a constant fraction that decay – here one-sixth. This constant-fractional-decay is the key idea.