Quick Lab
Modeling Half-Life
Procedure
Put 100 1-cm squares of wallpaper in a large plastic bag. Construct a data table with 2 columns and 9 blank rows. Label the columns Spill Number and Number of Squares Returned.
Close the bag and shake it to mix up the squares. Then, spill them onto a flat surface.
Remove the squares that are face-side up. Record the number of squares remaining and return them to the bag.
Repeat Steps 2 and 3 until there are no squares left to put back into the bag.
Analyze and Conclude
Analyzing Data How many spills were required to remove half of the squares? To remove three fourths of the squares?
Using Graphs Graph your results. Plot spill number on the horizontal axis and the number of squares remaining on the vertical axis.
Using Models If each spill represents one year, what is the half-life of the squares?
Suppose you have a one-gram sample of iridium-182, which undergoes beta decay to form osmium-182. The half-life of iridium-182 is 15 minutes. After 45 minutes, how much iridium-182 will remain in the sample? To solve this problem, you first need to calculate how many half-lives will elapse during the total time of decay.
After three half-lives, the amount of iridium-182 has been reduced by half three times.
So after 45 minutes, gram, or 0.125 gram, of iridium-182 remains while 0.875 gram of the sample has decayed into osmium-182.
Radioactive Dating
Now suppose you have a sample that was originally iridium-182, but three quarters of it have since decayed into osmium-182. Based on the fraction of iridium-182 left (one quarter), you can calculate the age of the sample to be two half-lives, or 30 minutes old.
The artifacts from Cactus Hill were dated by measuring levels of carbon-14, which has a half-life of 5730 years. Carbon-14 is formed in the upper atmosphere when neutrons produced by cosmic rays collide with nitrogen-14 atoms. The radioactive carbon-14 undergoes beta decay to form nitrogen-14.
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