## Experiment N-1

Chance:  A model of the hidden process

Nuclear and radioactivity are scary words for many people.  When we don't know enough to differentiate real hazards from false ones, our thoughts and efforts can be manipulated to unwittingly serve others' interests.  This series of experiments should help you better understand radioactivity so you can recognize situations of little hazard.  These experiments should also help you recognize significant radiation hazards and learn how to work safely despite such hazards.  Every atom has a nucleus!  Many of these nuclei occasionally spontaneously change on their own accord.  As a result, nuclear energy and radioactivity have been a natural part of the world all around us since creation.  So such radioactivity should not be viewed as a recent, man-made risk to civilization.  But because the forces inside a nucleus are stronger than chemical bonds, the energy of each event is greater and thus capable of more damage than chemical change inside a molecule.  So when we choose to use radioactivity for our purposes, we need to be aware of potential risks.

### Experiment

Many radioactive processes behave much the same as coin tosses.  So some of the properties of radioactivity can be modeled by tossing a bunch of coins.

1. Obtain about 100 coins.  (If you don't have 100 coins handy, you might use 20 coins, but do the procedure 5 times.  Then find the sum the first toss, the sum of the second toss, the sum of the third toss, etc. until you have all the sums of successive tosses which will be equivalent to having 100 coins and tossing all at once.)
2. Toss the coins.
3. Inspect each coin and remove any with the head showing.  This is as if the coins with heads up were radioactive and were no longer there, having changed to something else.
4. Count and record the number of remaining coins.
5. Repeat, returning to step #2 until no coins remain.
6. Construct a line graph in your journal of the number of coins after each toss verses the number of the toss (time).  Don't forget to graph the 100 coins that were present before the first toss (at time zero).

Note there is a pattern on the graph.  When is the change fastest and when is it slowest?  At first how many tosses were required to reduce the number of coins in half?  Later on how many tosses were required to reduce the number of coins in half?  If you had started with billions of coins, how many tosses would be required to reduce the number of coins to half the number?  This number of tosses needed to reduce the number of active coins in half is similar to the time for chance processes such as radioactivity to reduce the active material in half, called half life.  If you had started with billions of coins, how many tosses would be required to reduce the number of coins to zero?  The difficulty in calculating the total time is the reason that we use the half life to describe such chance processes.  Real radioactive materials also release most of their energy at first (so are most dangerous then), but continue to release energy at an much reduced (and safer) level over extended time.

Those who don't understand the significance of the shape of this graph often find this a cause for great concern:  For example they say, Radioactive waste materials are extremely deadly AND will last forever.  But the hazard of radioactivity comes from the release of energy.  And like the removal of coins, that is fastest (and most hazardous) at first.  After some time, just as the removal of coins slowed significantly, the release of energy is substantially reduced (so the hazard eventually becomes small).  So while radioactive waste materials can be very hazardous at first, after many half lives the danger becomes vanishing small.

Consider the related matter of the length of half life:  How would the graph be different if you had used dice with six sides but only removed dice with say four dots on top?  Only 1/6 would be removed on each toss.  (You might want to try to determine what the half life would be in this case.)  If the chance for nuclear change is less, the process is stretched out over longer time, but the rate of energy release (and danger) is reduced.  Substances with short half lives of radioactivity pose significant danger for only brief periods of time.  Substances with very long half lives of radioactivity pose very little risks even at first.  So in summary, the radioactive materials with highest decay rates (,the most dangerous,) last only briefly, while those with long lives will last nearly forever but pose almost no danger at all.

Communicating technical information such as observations and findings is a skill used by scientists but useful for most others.  If you need course credit, use your observations in your journal to construct a formal report.

created 11/8/2002
revised 7/9/2005
by D Trapp