In article o.uk, Dave
Liquorice wrote:
On Wed, 23 Sep 2009 22:57:12 +0100, Paul Martin wrote:


(*) I think, what does happen to the probabilty of an event after N half
lives? Gut feeling is that the probabilty increases but as for any given
half life period it's stuck at 50% I'm not so sure.

IIRC The easiest way to understand what (probably!) happens over N
half-lives is to say that its chance of *surviving* each half-life period
is 0.5. So the chance of surviving N of them is obtained by multipling 0.5
by itself N times. i.e. 0.5 to the power N.

So for 2 half live 0.5 x 0.5 = 0.25 survival - i.e. 0.75 chance of having
decayed, etc.

This also leads to the usual 'exponential' curves. From the POV of Physics
the atom obviously isn't (assumed to) be sitting there working out these
factors on a tiny subatomic hand calculator. :-) It just has a given
chance of decay during each brief period of time. That then scales as a
chance of survival according to the above rule, leading to the concepts of
'half life' and 'exponential decay' which are essentially consequences of
the chance of each atom surviving each brief time interval.

But as you pointed out, this is just the 'most likely' result in terms of
how many of a population of such atoms will survive. Actual number may well
be different to an unpredictable extent.

Slainte,

Jim

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