Re: Radioactive decay

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
> I just tried a hardware simulation using ten
> common pencils (hexagonal cross sections).

Excellent idea.

> Each pencil
> has a black spot labeled 2 HB on one of its sides. I threw
> all pencils on the flat table randomly and counted black
> labels facing up. (It is like throwing ten dice and counting
> one's).

Exactly so.

> The procedure was repeated ten times. The result were:
>
> 1, 1, 4, 0, 2, 1, 1, 2, 1, 3
>
> On the average 16 black spots or 1.6 per throw. I rounded
> this to 2 and removed 2 pencils.

I'm slightly confused at this point.  I don't see
the purpose of the repetition and averaging -- it
seems to be extra work, and the work is worse than
wasted, because it detracts from the otherwise-excellent
simplicity and immediacy of the demonstration.

Why not just toss the pencils and immediately snatch
away all those that land black-spot-up?

> I had no
> choice but to round fractional outcomes because pencils
> (atoms) are indivisible.

I disagree!  The indivisibility of pencils accuratly
models the indivisibility of atoms -- so why fight it?
Averaging detracts from the accuracy and from the
realism.

=============================

Tangential remarks:

1) If the decay rate of 16.66% per round is too fast, you
can lower it by various means.  You can lower it by a
factor of 4 by saying that they only decay if they land
black-spot-up _and_ pointing toward the north side of the
room.

2) Pennies in cups are cheaper than pencils.  Decay occurs
when the cup comes up all-heads.
 -- 4 coins per cup ==> decay rate = 6% per round
 -- 5 coins per cup ==> decay rate = 3% per round.

Another trick is to go to the hardware store and buy a box
of #2 washers.  Spray-paint 'em red on one side.  They have
the advantage of being small, so they fit into smaller
cups without overlap.  Also red-versus-shiny is easier
to see at a glance when you're in a hurry.