[dgt20 (OP)]

Why is the radioactive decay experiment consisting of rolling dice inaccurate?

Are there any other reasons other than dices only show a 1/6 chance while in real life decay probability is much more larger?

[Bored chemist]

I think the biggest problem is getting enough dice (incidentally, dice is the plural- one, on its own, is a die).
Also, the dice get thrown in batches, but decay is continuous.

[alancalverd]

Its "accuracy", i.e. the closeness of fit  to an actual decay curve, depends on the number of dice involved. If you start with 400 dice and eliminate all the 4,5 or 6 scores on each roll, the expectation* is that you will have 200, 100, 50 and 25 dice after 1,2,3 or 4 rolls. Problem is that the dice are entirely independent, so whether you have 12 or 13 after the next roll is a matter of chance. If you have 12, then subsequent rolls will  probably show a faster "decay", and 13 will show a slower decay than the expected rate.

If you want to simulate the decay of 1 gram of, say, ⁴⁰K, you will need 1.5 x 10²² dice (and roll them every 1.25 billion years, for complete realism!)


*Note that this is the central value of a random number. Things could go spectacularly "wrong" if the first roll left 190 or 210 rather than 200 dice, but the probability of doing so is quite high.

[Colin2B]

It's not the 1/6, you could do it with 1/12 sided dice and get same problem.
If I remember correctly you throw lots of dice and count 6s and say that is decay in 1s. It's the 1s that's the problem, during this time the real decay has been going on continuously from time 0.
It's a bit like compound interest in reverse, work it out in 1 year blocks or 1 month blocks and you get different answers.

EDIT: Whoops message collided with Alan's. Different way of calculating the granularity but same result.

[dgt20 (OP)]

o

So would talking about how 100 dices inst accurate enough to represent a decay in real life be worthwhile and that if the experiment was to be more realistic it would be recommended to use  more dices?

[Bill S]

Things could go spectacularly "wrong" if the first roll left 190 or 210 rather than 200 dice, but the probability of doing so is quite high.

So, what made anyone think this was a good idea, in the first place?

[alancalverd]

It's a fair demonstration of the meaning of half-life and exponential decay, provided that you begin with enough dice and don't look too closely at the results. With all digital simulations, there is an element of coarseness due to "discretisation error" that can in the worst cases lead to instability and a failure to converge at all. The nuclear decay dice game will always converge but the difference between model and reality, or even repeat model runs,  can be quite striking because the reality, though inherently discrete, usually involves zillions of nuclei.

For a classroom demonstration, any number more than about 300 dice will give a convincing demonstration of both randomness (give each kid 10 - 20 dice to begin with , and look at the range of individual scores after the first throw) and exponential decay with a half-life of one throw (if you discard 4/5/6) or three throws if you just discard 6s.