Demonstrating Half-life
Materials: 100 pennies, box
Procedure:
1. Place 100 pennies in a shoe box so that all are heads up, laying in a flat single-file pile.
2. Shake the box up and down at least five times so that the pennies have a chance to flip around and change sides.
3. After shaking, count and remove all the pennies that are tails up.
4. Record on your data table the number of pennies remaining in the box.
5. Repeat steps 2-4 until only one penny remains.
6. Graph your data.
Shakes
(time)
(x)
0
Pennies
in box
(y)
100
5
10
15
20
25
30
35
40
45
50
Conclusions:
1. What is the difference between relative and absolute/radiometric dating?
2. What fraction of the remaining pennies was removed from the box after each shaking? ___________
3. How many times did you shake the box before only one penny remained? ____________
4. If someone stopped you when you had 12 pennies remaining, how could they have calculated the time (in # of
shakes) you started the experiment?
5. If you started with 5731 pennies in the box all heads up and you did the same procedure, how many half-lives would
it take you to reach 89 pennies? Show your work.
6. The half-life of uranium is 4.5 billion years. If you have a sample of uranium that weights 55 grams and the earth is
believed to be 4.5 billion years old. How much uranium did your sample contain when the earth was formed?
Calculating Half- Life Problems
Example: An isotope of cesium has a half-life of 30 years. If 60 g of cesium disintegrates over a period of 120 years, how
many grams of cesium would remain?
How to calculate:
1. Draw a T-Table.
2. Label the left side with the unit of time mentioned.
3. Label the right side with the mass mentioned in the problem.
4. Begin by ALWAYS writing a 0 in the time column.
5. Then, in the time column, add one half-life at a time till you
reach the total time given in the problem.
6. In the mass column, always start with the mass originally
given in the problem.
7. The keep dividing the number in each mass column by 2 for the
number of half-lives on the left column.
8. Rules: Add the half-lives on the left, divide by 2 on the right.
9. The number of times you divide, equals how many half-lives.
10. The number on the right is the amount of mass remaining.
PROBLEMS: SHOW YOUR WORK ON A SEPARATE PAGE – ANSWERS BELOW
1. Radium has a half-life of 1,600 yrs. If we start with 8,000 g of radium, how much will be left after 6,400 yrs.?
2. Gold has a half-life of 3 days. How long does it take a 180 g sample to decay to .175 grams?
3. The half-life of cobalt is 3.8 days. How much of a 250g sample is left after 19 days?
4. The half-life of iodine is 8.07 days. If 25g are left after 40.35 days, how many grams were in the original sample?
5. The half-life of barium is 2 years. How many years would it take for a 4 mg sample to decay to .5 mg?
6. Selenium has a half-life of 25 minutes. How many minutes would it take for 10 mg to decay and only have 1.25
mg remaining?
7. The half-life of Potassium is 3 minutes. How much of a 48 gram sample remains after 15 min?
8. The half-life of iodine is 4.23 days. If 250g are left after 25.38 days, how many g were in the original sample?
EXTRA CREDIT: If 100 g of silver decays to 6.25g in 10.8 days, what is the half-life of silver?