Iron Science teacher February 14 2004

Battle Chocolate.

Modelling Radioactive Half-Life using M+M's

Begin with 64 M=M's, it is best if they are all one color.

Take a cup that will hold all of the M+M's.

Shake them up in the cup and dump the M+M's onto a clean piece of cloth.

Notice that some M+M's have the M+M logo showing, while others show a blank backside.

Remove all of the blank side M+M's and arrange them in a vertical row at the left edge of a piece of paper. About half of the M+M's will be removed on this first throw.

Pick up all the remaining M+M's and return them to the cup. Shake them up and throw them again. Remove the one's that have "decayed," that is the ones that show their blank side. Arange them in a vertical column just to the right of the first column. Notice how the second column is shorter than the first.

Repeat the shaking and sorting 5 times.

Notice that each cloumn is about half as high as the previous one.

What's Going On?

There is a 50-50 chance that an M+M will land with its logo side up. About 1/2 the M+M's will decay at each throw. Once they have decayed they are removed from the active M+M pile and can no longer decay. So after the first shake there are only about half of the M+M's left to decay. After the second shake a quarter, then an eight and so on.

The time it takes for half of an initial collection to decay is called its half-life.

So What?

Radioactive atoms decay into other atoms. Uranium decays into lead for example. These radioactice decays have a halflife, the decay of Uranium 238 to lead has a half life of about 4.5 billion years.

When the Uranium in incorporated into a crystal in a rock, chemistry sorts out the atoms so that the crsytal starts with all Uranium atoms and no lead atoms. After 4.5 billion years half of the Uranium atoms have radioactively decayed into lead atoms. On earth and in meteorites about 1/2 of the Uranium has decayed into lead meaning that the Earth and meteorites were formed about 4.5 billion years ago.

Going Further

Try to find the half-life of other candies:

Cubes such as Fudgies, rectangular solids such as Starbursts even cones such as Hershey's Kisses.

Off the Wall

Radioactive Decay and tooth decay

Semi-Log plot a straight line this is a really sweet way to plot data.

A semi-sweet log plot.


Scientific Explorations with Paul Doherty

© 2004

11 February 2004