POLONIUM - 210
After completing this worksheet you should:
• understand that radioactive decay is a random process
• understand the meaning of “half-life”
• be able to model radioactive decay
You will cover EXCEL skills:
In 2006, Alexander Litvinenko fell ill. Three weeks later he tragically died as the first victim of
the radiation effects of polonium-210. The amount of polonium ingested was tiny, probably
about 10 micrograms, about one tenth the mass of a grain of salt.
In this worksheet, you will estimate the fraction of the ingested polonium-210 that had
undergone radioactive decay during the 3 weeks until his death.
Radioactive decay is a random process. We will use the spreadsheet to
simulate a die and use the throw of a die to decide if a nucleus decays, or not,
during a specified time period. We will start by producing a six-sided die which
produces numbers 0 to 5. If a 0 is thrown, the nucleus decays.
Step 1
1
A
B
No. die sides =
6
2
0.3416
3
2
Name this cell “DieSides”
=RAND()
=INT(DieSides*B2)
• Complete the cells as shown.
• Hit F9 on the key board. Note
“=RAND()” in cell B2 produces
a random number between 0
and 1.
• The command in B3 produces
an INTeger (whole number) 0 to
5, like a 6-sided die.
At each time step, a die will be “thrown” and a “0” will indicate that the nucleus has decayed.
So, at each time step, each nucleus will have a one in six chance of decaying.
=E1+1
Step 2
1
D
E
F
G
Time (days)
0
1
2
1
5
0
• We will consider a time period of 21
days. Enter cell D1 as shown, 0 in E1
and the formula shown into F1. Select
cells F1 to Z1 and “fill right” (<ctrl>R).
• We will model 100 nuclei. Enter cells D4,
D5 and the formula in D6. Select D6 to
D104 and fill down.
• Enter “1” into E5. This means the
nucleus has not decayed at time 0
• Enter the IF command into F5. Select F5
to Z5 and fill right.
2
3
4
Nucleus
5
1
6
2
=D5+1
=IF(E5=0,0,INT(DieSides*RAND()))
=(If nucleus has decayed at previous time step, it stays decayed, otherwise throw the die)
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Step 3
1
2
D
E
F
G
Time (days)
0
1
2
100
76
59
No. nuclei
Notice the sequence of numbers for nucleus 1. Here we
have 1,5,0,… but yours will be different and will change
every time you hit F9.
The “1” is arbitrary – it indicates nucleus 1 has not decayed.
3
4
Nucleus
5
1
1
5
0
6
2
1
4
1
7
3
1
3
3
The “5” is the random throw of a die at day 1 for nucleus 1.
The “0” is a random throw of the die at day 2 and indicates
that nucleus 1 has decayed. All other cells H5, I5 etc will
read “0”.
=COUNTIF(E5:E104,"<>0")
•
•
•
Select cells E5 to E104 and fill down. All nuclei start with a “1”.
Select cells F5 to Z104 and fill down AND fill right.
Finally, enter the command shown into E2, select E2 to Z2 and fill right.
Step 4
Decay Curve
Hit F9 a few times to see how this changes
the graph. Notice how the points move each
time, but the overall shape of the graph
stays the same.
120
Undecayed Nuclei
Select cells E1 to Z2 and plot a scatter
graph. This will show how the nuclei decay.
100
80
60
40
20
0
0
5
10
15
20
25
T ime (days)
QUESTIONS
1. For Polonium-210, the chance of a nucleus decaying in one day is about 1 in 200. Use a
200-sided die to estimate the fraction of Polonium-210 that remains after 3 weeks. Why
should you do several simulations (hit F9) and average your result?
2. Change the time scale to “weeks” rather than “days” by using a 29-sided die. Why 29?
Approximately how many weeks does it take for half of the nuclei to decay?
3. How many weeks does it take for half of the remaining 50 nuclei to decay?
4. Polonium-210 emits alpha particles. Explain why Polonium-210 is virtually harmless unless
it is ingested.
NANOCLIP
The publicity surrounding Alexander Litvinenko’s tragic death
resulted in numerous television and radio appearances by
Surrey’s nuclear physicists, including Paddy Regan. Explaining
the science to the general public is a difficult task!
Young nuclear physicists such as Amy Bartlett are modelling nuclear processes inside a
star. This is to solve one of the biggest questions science still has to answer - how were
all of the heavy elements in our universe made?
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