Half-Life: The Penny Model

If you're introducing your students to the concept of half-life, things are probably seem a bit fuzzy for them.  Let them get some hands-on experience and see if things don't come a bit easier.

A quick review for anyone who may not have done this in awhile...
...half-life is the amount of time needed for half of the atoms in a sampleof a radioactive isotope (one form of an element) to deacy, or reach a stable state.  Some isotopes have half-lives that are a matter of seconds - they decay and become stable rapidly.  Other isotopes have half-lives that are thousands of years. 

Now, on with the show!

Start with 100 pennies.  Put them all in a cup, place your hand on the top and shake.  Dump the pennies out onto the table.  Remove all of the pennies with heads up (or tails, it doesn't matter, just pick one and stick with it).  Count and record the remaining pennies.  You have just completed one half-life.  Repeat until you are down to one or no pennies. 

Have students graph their data.  It's always good to practice graphing, and it helps some students visualize what's happening (and the graph for half-life will always take the same shape - the numbers and units on the axes may change, but the shape of the curve is always the same).

Now you can pose some questions to your students....
If someone walked by and saw that you had 7 pennies remaining, could they determine how many half-lives (shakes) you had completed?  How? 

And then take it into the real-world application of carbon dating....
Imagine that while digging in your yard, you uncover what appears to be a very old bone.  Through the help of a scientist at the lab, you're able to learn that the bone contains 12 pug (picomicrograms) of carbon-14 and that it contained 100 pug of carbon-14 when it was buried.  Carbon-14 has a half-life of 5730 years.  How old is the bone. 

P.S.
I did come across one criticism of this activity online, and I thought it was worth mentioning.  This person suggested that you needed to replace the "decayed" pennies with something else, because they decay, they don't disappear.  I thought it was a valid point, and in thinking about it was a little surprised that I've never seen that mentioned as a part of the activity. 

I'm thinking the small counting chips that you might have for games of bingo would be great - a similar size but definitely different from pennies would work great.  Kernals of popcorn would also be an inexpensive item to use.  Let me know if you think of something else. 

P.P.S.

If your students have been super good (or it's immediately following Halloween and you have a plethora of left-over candy), you could also complete this activity using M&Ms or Skittles.