Embedded Files
Radiation
Radiation
Radioactive decay is a random process. In a sample of radioactive material, there are lots and lots of nuclei. We can't predict which nucleus will decay next, or when any particular nucleus will decay, and not all nuclei will decay at the same time. Instead, we know that a certain number of nuclei will decay in a certain time. The time taken for half the unstable nuclei in a sample to decay is called the half life, (t1/2).
There are two important definitions of half life:
The time it takes for the number of radioactive nuclei in a sample to decrease by 50%.
The time it takes for the activity/count rate of a radioactive source to decrease by 50%.
We cannot affect the half life of an isotope - changing the temperature or pressure, for example, make no difference. Some isotopes have very short half lives of only a few seconds, whilst others can be thousands of years.
One application of half lives is Radiocarbon Dating. This is the process of determining the age of a previously living object by measuring the ratio of carbon-14 to carbon-12 present, (carbon-14 is unstable, and decays to nitrogen-14, whereas carbon-12 is stable). This is explained by Archaeologist Dr Penny Bickle from the University of York in the video below.
Modelling Half-Lives with Dice
Modelling Half-Lives with Dice
Just like radioactive decay, rolling a die is also a random process. We can therefore use dice, or anything else that has different sides such as coins (or sweets such as Skittles or M&M's) to model radioactive decay.
In the loan kit, we provide 15 bags that each contain 100 6-sided dice, (if you are missing any dice, please do let us know).
We can change the "half-life" of the system by changing the condition for decay, i.e. how many dice are expected to decay in each step. For example, if the dice show an odd number, we can say these dice have decayed. As this should be 50% of the dice, this means the half-life of the system is one throw.
Count the number of dice that you start with - these are your unstable nuclei.
(Note: Each bag should contain 100 dice)
Record this number in a table for time t = 0.
Place the dice in the black bag and shake them;
Pour the dice (carefully) onto the table;
Count any dice with an even number, (i.e. 2, 4, 6) facing up.
These represent nuclei that haven’t decayed yet;
Record this number in your table for time t = 1 and put these dice back into the bag, (e.g. N = 47);
Put any dice showing an odd number, i.e. those that have decayed, to one side.
Shake and throw the dice again, keeping and recording any dice that land on an even number up (and discarding the rest)
Repeat until all your dice have decayed!
Now plot a graph of the time along the x-axis and the number of radioactive nuclei on the y-axis.
Find the half life of your dice (or other objects) by reading off the time when half of your dice have 'decayed'.
To improve the accuracy of the half life, take another two points on your graph where the number of unstable nuclei have halved and take an average of your two half lives.
Teaching Material
Teaching Material
Pre-16 Masterclass
Pre-16 Masterclass
Module 2: Properties of Radiation
In the Pre-16 Masterclass, the students are asked to plot the graph using sweets to model the unstable nuclei. Calculation questions are included - these do not use the equations for half-life and there is no expectation to use exponentials. A video explaining how half-lives are used in carbon dating is included (with archaeologist Dr Penny Bickle).
Post-16 Masterclass
Post-16 Masterclass
Module 1: Decay Modes and Energy
The Post-16 Masterclass includes an activity modelling radioactive decay using the random number generator in Excel (or Google Sheets). Equations for half life are derived and questions cover use of exponentials. A video explaining carbon dating is also included (with archaeologist Dr Penny Bickle).
Class Worksheets
Class Worksheets
When using the dice with your classes, you may wish to use the worksheets below to investigate half-lives. There are three documents: a Pre-16 student worksheet, a Post-16 student worksheet, and an accompanying teacher document:
Isaac Physics Questions
Isaac Physics Questions
You can find some Isaac Physics questions you can set to your students related to half-lives and decays below. Please feel free to look at our page for help setting up an account on Isaac Physics!
Note: the "Modelling Radioactive Decay" questions use the Excel/Google Sheets/Python activity, found in the "Modelling With Random Numbers" section below.
Useful Links
Useful Links
Modelling With Random Numbers
Modelling With Random Numbers
Another way to investigate radioactive decay is using random numbers generated in Excel or Google Sheets. One of the activities in the Post-16 Masterclass is to model radioactive decay using a random number generator in a spreadsheet. Instructions are available for Excel or Google Sheets:
Alternatively, if you have any students with an interest in coding, they can carry out the same exercise using Python:
Interesting Papers
Interesting Papers
Why is the half-life in the dice experiment 'slightly wrong'?
The 'radioactive dice' experiment is a commonly used classroom analogue to model the decay of radioactive nuclei. However, the value of the half-life obtained from this experiment differs significantly from that calculated for real nuclei decaying exponentially with the same decay constant. This article attempts to explain the discrepancy and suggests modifications to the experiment to minimize this effect.
Murray A, Hart I. The ‘radioactive dice’ experiment: why is the ‘half-life’ slightly wrong?. Physics Education. 2012 Mar 1;47(2):197.
If you are having trouble accessing this paper, use this link to a PDF version of it.
Cool probabilistic things we typically don’t teach our students about radioactive decay, but should
If you have any students who are interested in the mathematics behind the statistics of radioactive decay, there is a great paper by David Jon Furbish at Vanderbilt University that they may be interested in reading. Radioactive decay is a rich topic whose implications and applications appear in many fields of science. Moreover, because of its familiarity, radioactive decay is a nice entry into the broader topic of stochastic processes. The idea of a Poisson process in particularly is a lovely starting point for considering a variety of stochastic processes that occur in natural and engineered systems across many scales.
Furbish DJ. Cool probabilistic things we typically don’t teach our students about radioactive decay, but should.
If you are having trouble accessing this paper, use this link to a PDF version of it.
Page updated
Report abuse