HALF LIFE
ANALOGUE
LA60-010
INSTRUCTIONS FOR USE
RADIOACTIVITY DECAY ANALOGUE
LA 60-010
INTRODUCTION
This simple apparatus provides students with an interactive
investigation into the complex topic of random nuclear decay in a
completely safe and enjoyable way. The results are reliable and give
the opportunity for graphical work following a whole class activity - a
welcome change from teacher demonstrations in the topic.
APPLICATIONS
Radioactive decay
Half-life
Statistical probability
Graphical analysis
GENERAL DESCRIPTION
The apparatus consists of 500 small plastic cubes, each with one painted surface.
If a cube is repeatedly thrown on to a flat surface there is a 1 in 6 chance of the
painted side landing uppermost. In the decay analogue we imagine that each
cube represents an atomic nucleus and assign the process of nuclear decay to the
landing of the cube with the painted surface upwards. If 60 cubes were thrown
together we would expect 10 of them to land in this way and we would say that
10 nuclei had decayed. These 10 nuclei would no longer be available to decay so
they are removed from the pile. If the remaining 50 cubes are thrown we would
expect about 8 to “decay” and these are again removed prior to the next throw.
Of the remaining 42 cubes, about 7 should decay next throw and so the process is
continued until all the nuclei have transformed.
TYPICAL CLASSROOM PROCEDURE
To involve everyone in the investigation first explain that each cube represents
an atomic nucleus and when it is thrown on to the bench it can be said to have
decayed into a different nucleus if it lands with the painted side uppermost.
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Divide a class of 30 students into 10 groups (fewer groups if there are
fewer students) and give each group approximately 50 cubes, preferably
in some container such as an ice-cream tray or cardboard box etc.
Give one student a calculator to add up the scores and write them on the
board.
Instruct the groups that they should gently “throw” the cubes on to the
bench when you say so and that they should then count the cubes which
land painted side upwards and move them to one side.
The student at the front asks each group in turn how many cubes
“decayed” and these are added up to give a score for throw number one.
The score is recorded on the board in three columns:
TOTAL DECAYED No. REMAINING.
THROW No.
The students gather together the remaining, undecayed cubes and repeat
the process when the signal is given. The process is repeated until there
are no more cubes left to throw.
P.T.O.
ANALYSIS
The third column is calculated by subtracting the number decayed from the total
number of cubes. Typical results would be:
TOTAL DECAYED
No. REMAINING
THROW No.
0
0
500
1
82
418
2
71
347
3
58
289
etc
From the tabulated data on the board students draw a graph of No. REMAINING
(y-axis) against THROW No. (x-axis)
The graph should be a good approximation to an exponential decay curve.
Students can be asked to find how many throws were required to reduce the
number of cubes to half the original number and then half again etc (fractions of
a throw are allowed) and the concept of half-life introduced.
In the real world “throw” is replaced by time and half lives of typical nuclei can
be discussed.
NOTES
The experiment relies on probability and as such the results will not give a
perfect line for the graph. The results for each throw are recorded accurately as
given and a best fit line through the points is drawn.
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