Re: Radioactive decay

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

"John S. Denker" suggested:

> ... take the data _without_ averaging.  Record the decay
> sequences, fluctuations and all.  Observe that the decay
> is approximately described by an exponential, but with
> fluctuations above and below. Repeat the process.
> Take the average, or (better) the sum.

I agree that sums are better than averages and recording
outcomes as they are (instead of averaging at each step)
is more to the point. Here are my new data. The first
column is the trial number. The next seven columns are
samples of sequences. They show, for example, that
after 6 throws the numbers of remaining pencils were:
4, 3, 2, 4, 5, 4 and 4. The last column shows the sums.
Seven samples are not as good as 25 would be (one
from each student) but by plotting their sums I can
already see that the half-life is between 3 and 4
time units, as it should be for lambda=1/6.

i                                                 sum

0    10    10    10    10    10    10    10        70
1     7     6     8    10     8     9     9        57
2     6     5     7     8     7     7     8        48
3     6     4     6     7     7     7     7        44
4     4     3     6     6     5     5     6        35
5     4     3     5     5     5     5     5        32
6     4     3     2     4     5     4     4        26

The end result is the same as before but there is no need to truncate
fractions. That is a big improvement. I still think that this simulation
is nothing else but an illustration that the exponential decay is a
consequence of the constancy of lambda (individual atoms have no
age, shapes of pencils do not change). Rightly or wrongly many
authors refer to the exponential formula as the "low of decay." This
point is not worth arguing now, IMHO. I hope these suggestions
will be useful to some teachers. Naturally, each will enrich the activity
to match the objectives. Studying fluctuations may be one of them.
Ludwik Kowalski