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Time to play with dice (this is not for crap shooting). You will be given a number of dice. Your job is to roll the dice and, as they fall to the table, remove from the pile all dice that have the number 3 (or whatever number your instructor tells you to use) showing. Keep track of the roll number and the number of dice left after roll. Roll the dice down to less than 6 dice, put the dice back together, re-roll the dice and keep track again (do 10 trails). Total the number of dice left after each roll and then plot a graph of the total number left after each throw (N) vs. the throw number.

You should remember that this should be a smooth curve and does not
need to
go through every point, just close. This will give you a decay curve
for dice.
Determine the half-life of the dice by looking at your graph. How many
throws
(to the nearest quarter of throw) does it take for half of the dice to
be gone?
(i.e. If you started with __1000 __dice (**N _{0}**) how
many
throws would it take for

Attempt to obtain 5 half-lives. Take the first half-life divided by
one, the
second half-life divided by two, the third half-life divided by three,
etc. and
average these numbers. This number is the half-life **(T)** of the
dice and,
since **0.693 / T** (__Why?__) is the decay constant (the
probability of
decay per "throw number"), you should be able to calculate the
probability of decay for a particular die and compare this to the
actual value.

Now for some more fun stuff. Find the ratio **N/N _{0} **for
each
of your trials (

Take a sheet of 2-cycle semi-log paper (the reason it is called
semi-log
paper is because it is made from a part of tree logs) and plot the
ratio **N/N _{0}
**(found in the last part) vs. the throw number. Now, by doing a
careful
analysis, take the slope of this line. Remember that

__Wasn't that fun?__ I thought so. Here's the next part for fun
and games,
take __100 __key board keys and repeat the exercise in the first
paragraph.
However there are three possibilities. ('break' up, 'break' down, and
sideways)
You will be assigned one possibility, roll __10__ trails and plot
data as
before. Draw as many conclusions as you can from this data. Check with
other
groups to compare your data. Are the results nearly the same? If not
why not?

With cubes as simulated molecules, you will attempt to verify some
of the
principles of radioactive decay. Starting with a given number of
plastic cubes
that have a hole through them, throw the cubes onto a suitable surface
and
remove every cube that shows a hole on the top. It may be necessary to
carefully
move some of the cubes so they are not stacked on top of each other.
Replace
each of these 'decayed molecules' with a plastic die. Do this again,
replacing
each 'hole' cube with a die __but__ also removing each die that
lands with a
6 on top. Your data table will probably have at least five columns:

**Throw Number # Holes
Removed
# Holes Remaining # Dice Removed #
Dice
Remaining**

Continue to throw and replace/remove them as fast as possible until
less than
10 dice are left. Repeat this entire process several times. Plot two
graphs on
the same axis: total 'hole' cubes vs. throw and total dice vs. throw. (__Note__:
total dice vs. throw number should start at zero, increase, reach some
maximum
and then go back down. WHY?) You should remember that these curves
should be
smooth curves. How does this experiment compare with one measuring
normal
radioactivity with Geiger counters and other electronic equipment?

**References**

__Dice Shaking as an Analogy Radioactive Decay for First Order Kinetics__by Emeric Schultz [Journal of Chemical Education**74**505 (1997)] http://jchemed.chem.wisc.edu/Journal/issues/1997/may/abs505.html.- Radioactive Decay Curve by Alan L Tobecksen, IIT SMILE program interactive lesson. http://www.iit.edu/~smile/ph9495.html.
- The Probability of Rolling Dice: http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/intro_prob_models.html.
- Simulating Radioactive Decay: http://serc.carleton.edu/quantskills/activities/MandMModel.html.
- Mathematical Models of Radioactive Decay: http://www-math.mit.edu/~djk/calculus_beginners/chapter12/section02.html.
- Probability and Randomness: http://www.shodor.org/interactivate/lessons/ProbabilityGeometry/.
- Error Analysis: http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html.

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