Re: [Phys-L] mechanical simulation error (dice vs. nuclear decay)

[John Denker <jsd@av8n.com>]

On 11/18/2015 03:00 PM, Bernard Cleyet wrote:

> > The 'radioactive dice' experiment: why is the 'half-life' slightly wrong? - IOPscience 
> >
> > http://iopscience.iop.org/article/10.1088/0031-9120/47/2/197/meta

That's the most repulsive thing I've seen all day, and it's
been a really bad day.

The article is 2500 words long, and fails to obtain the right
answer.  Let's see if I can do better.


==============================
Let λ be the fraction removed in unit time.  So by definition:

   1/2^(1/τ) = (1 - λ)               [0]

where τ is the half-life.  Hence

         log(1/2)
   τ = -----------                   [1]
        log(1 - λ)

as you can easily rederive and/or easily verify.  Hint: try λ = 3/4.
Remark:  In the limit of very small λ, this reduces to:

         ln(2)
   τ = -----------                   [2]
           λ

as you can verify by expanding [1] to first order.  Murray and Hart
were mystified when they used [2] with a not-sufficiently-small λ.

Conclusion:  When in doubt, use [1] not [2].
============================



I think my version is shorter, more correct, and more useful. 

Tangential remark:  Note that in equation [1] I left the
base of the logarithm unspecified.  You can use log2, ln,
log10, or whatever you like.