Half of Half

Activity
Half of Half
Purpose:
To develop an understanding of half-life and radioactive decay.
Required Equipment and Supplies:
● shoe box
● 200 pennies (or equivalent)
● graph paper
Optional
Graphing calculator
Discussion:
Many things grow at a steady rate, such as population, money in a savings account and the accumulated
thickness of a sheet of paper that is continually folded over onto itself. Many other things decrease at a
steady rate, like the value of money in the bank, charge on a discharging capacitor and the amount of
certain materials during radioactive disintegration. A useful way to describe the rate of decrease is in
turn of half life – the time it takes for the quantity to reduce to half its value. For steady decrease,
called exponential decrease, the half life stays the same.
Radioactive materials are characterized by their rates of decay and rates in terms of their half lives.
You will explore this idea in this activity.
Procedure:
Step 1: Place more than 100 pennies in the shoe box and close the lid on the box. Shake the box for
several seconds. Open the box and remove all the pennies head-side up. Count these and record the
number in the table. Do not put the removed pennies back in the box.
Total Pieces
Shake
Number
Number of
pennies removed
Number of
pennies remaining
Shake
Number
Numbers of
pennies removed
Number of
pennies remaning
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Activity
Step 2: Repeat Step 1 until one or no coins remain in the shoe box. Record the number of pennies
removed each time in the table.
Step 3: Add the total the total number number of coins removed to find the original number of coin.
Now subtract the number of of coins removed each time from the total to find the coins remaining after
each shake.
Step 4: Graph the Coins Remaining vs. Number of Shakes. Plot the data and draw a smooth line that
best fit the points.
Summing up:
1. What is the interpretation of the graph you obtained?
2. About what percent of the reaming coins were removed on each shake and why?
3. Each shake represents a half-life for the coins. What is meant by half-life?
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Activity
Going further:
● Plot your data using your graphing calculator. Find the equation for the best-fit line.
●
Instead of using pennies, we could have used 100 dice and removed those that show a '3'. How
would the half-life compare to the pennies? What if we removed the ones that came up with a
'1' or a '6', how would this half-life compare to the pennies and to the half-life of the time when
we just removed the '3s'?
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