Rolling radioactive dice Decay and half life Rolling radioactive dice

Will it or won’t it? Imagine a radioactive sample… …now pick one unstable nucleus in the sample. Will this nucleus decay in the next second? What about in the next 10 million years?

Random The answer is: we can’t say for sure. Radioactive decay is a random process. This means it can’t be predicted – just like the roll of a dice. If you roll a die will it land with the six facing up? It’s impossible to know for sure.

Probability We can say how likely it is to roll a six though. The chances are 1 in 6. This probability helps us predict how many sixes will turn up if we roll 1000 dice. We can predict that about 167 of the dice will show a six.

Enough about dice… We can consider radioactive decay in terms of probability too. Different radio-isotopes have different probabilities of decay. But… For any sample of a particular radio-isotope (whether it’s a ton or a teaspoon) it takes the same time for half of the unstable nuclei in the sample to decay. This time period is known as the half life of that particular isotope.

Imaginary example Consider the isotope Madeupium 133. Suppose it has a half life of 10 minutes. A sample with 100 unstable nuclei to start with would have 50 left after the first 10 minutes. How many would be left after 20 mins? How many after 1 hour? (Not a real isotope) After 20 mins there would be 25 left (approx). After 1 hour there would be 1 or maybe 2 left.

Now try this one…

Neat theory, but does it work? Time (mins) Unstable nuclei remaining 140 1 2 3 4 5 6 First try it with dice… Take 140 dice and use it to model a sample of a radio-isotope. Roll all of them at the start. (Each roll will represent 1 minute passing) Take out all of the sixes and keep them separately. Count the remaining ones. Roll the remaining dice to represent the next minute. Record data in spreadsheet.

Now plot a graph – called a decay curve. Count Time 1 half life

Half life It’s the time taken for half of the radioactive nuclei in a sample to decay.

In real situations… (not involving dice) With real radioactive samples, clearly there is no way to count the number of unstable nuclei – there are billions. Fortunately there is a way to determine the half life though…

Measuring background radiation First use a GM tube and ratemeter to measure the background count. This is the number of decays per second detected due to background radiation, i.e. from the sources in the pie chart on the next slide.

Then... Bring the radioactive source close to the GM tube. Measure and record the count rate at regular intervals. Subtract the background rate from each one (to get the number of decays just from the source that we’re testing) Plot a graph of count rate against time. Because the count rate is proportional to the number of undecayed atoms, the graph will be a curve like the dice one. You can find the half life in the same way as before.

Now plot a graph – called a decay curve. Count Time 1 half life