Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: dgt20 on 03/03/2018 12:48:21

Say for the the number of parent isotopes left from the dice experiment at the 2nd time interval was 716 and the carbon 14 decay at the 2nd time interval is 924. Is it a valid comparison or because there isnt a decay constant for the dice experiment you cant compare the two? If you made the decay constant for the dice experiment 1/6 (0.166) and calculated the results would you be able to compare the dice results and carbon14 decay?

Depends on the time interval. t_{½} for ^{14}C is 5730 years giving a decay constant of 1.21 x 10^{4 }per year. The decay constant for 1/6 dice is 0.166 per throw so if each iteration equals 1372 years you will probably end up with something close to the halflife of ^{14}C
As others have pointed out, one problem with a small number of dice is the discretisation error. A simple calculation with Excel will give you a very smooth curve that looks like the real thing, but if you substititute ROUND((B2*5/6),0) for the first calculation et seq, you will get a series of integer approximations that look like real numbers of dice, and you may see the convergence problem if you vary the starting number by just a few  the tail of the curve will wag.

And don't forget that "1 in 6" is only true as the mean for an infinite number of throws. It is entirely possible for a given throw to produce no 6's or all 6's in practice. One or two early throws that depart significantly from the mean, will seriously distort the subsequent convergence.