Naked Science Forum

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

Title: Can carbon-14 decay and dice experiment decay results be compared?
Post 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?
Title: Re: Can carbon-14 decay and dice experiment decay results be compared?
Post by: alancalverd on 03/03/2018 13:53:45
Depends on the time interval. t for 14C 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 half-life of 14C

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.
Title: Re: Can carbon-14 decay and dice experiment decay results be compared?
Post by: alancalverd on 04/03/2018 00:03:16
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.