Lab Activity - Simulate Half-life with M&Ms

Radioactivity - Mmmm & Mmmm, Good

Purpose:

Radioactivity was a phenomena that helped change the nature of science as the twentieth century began (helped lead to fundamental changes in chemistry, nuclear physics, biology, archeology and geology).  And one of the most important ideas to come from the studies of radioactivity is the concept that it is a statistical and probabilistic process.  This means that one can apply statistical and probabilistic methods to the study of radioactivity, and one of those statistical measures is the half-life.  You will begin to gain understanding of half-lives by using some pretty sophisticated equipment.

Equipment:     M & M’s (pretty sophisticated, huh?!)

Procedure:

Work your way through the following questions with your M & M’s; choose one side of your M & M’s to represent a ‘living’ radioactive atom, and the other side to represent a decayed atom that will be removed from your sample.  Dump your ‘living’ pieces on your table and remove those that have just decayed. Continue this until all have decayed.

Questions and Analysis:

1.       Make a data table to keep track of how many M & M’s decay each time you dump them on the table.  Make sure to count the original number of pieces before you begin.  After all the pieces have decayed, make a graph of the number of pieces left after each ‘half-life’ versus the number of the turn you dumped them.  Is the shape of your graph linear?  If not, how would you describe it?

2.       The half-life for carbon-14 (this is an isotope of normal carbon-12; it just has two extra neutrons that make it radioactive) is about 5700 years.  What does this mean if you have a sample of 1000 carbon-14 atoms?  What does this mean if you have a single carbon-14 atom?

      3.   Make a graph of the number of carbon-14 atoms (suppose you have an initial

            sample of 1000 atoms) as a function of time, knowing the half-life is 5700 years. 

            For an initial sample of 1000 carbon-14 atoms, approximately how long would it

            take to have only 100 carbon-14 atoms remaining from the original sample? 

           Make your approximation from your graph.  Then, calculate it from the decay law:

          N  =  N_oe^{- t / t}

          where t = t _½ / ln2; this is sort of like an average time that is used for radioactivity

          and is different for each radioactive material.  Work together to figure this out, just

          like a biologist or archeologist would have to do.  Some call τ the decay constant or

          time constant for the material being considered.  We will see time constants again for

          certain types of circuits in E&M.

4.  Explain how scientists can use carbon-14 as a way of measuring the age of bones.  

     Would you trust carbon-14 dating for objects that may be millions of years old? 

     Why or why not?

5.       Name three other phenomena, events, activities, etc., that require probability to

     describe them.  Also, in your own words, define “probability.”

Above and Beyond: If curious, check out details about radiometric dating techniques and the math behind those techniques.