Re: Halflife and Randomness
- From: Timberwoof <timberwoof.spam@xxxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 12 Jul 2007 16:24:23 -0700
In article <1184277085.106106.315430@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Robert Carnegie <rja.carnegie@xxxxxxxxxx> wrote:
Ernest Major wrote:
In message <5fmc66F3cgqb4U1@xxxxxxxxxxxxxxxxxx>, alwaysaskingquestions
<alwaysaskingquestions@xxxxxxxxx> writes
Third issue is that although the rate of decay measured in terms of
halflife
is constant the rate measured in atoms per second is exponential and
therefore constantly changing i.e. in the example above the average decay
rate during the first 10 seconds is 3.2 per second, during the next 10
seconds it is 1.6 per second and so on, so we cannot even say what the
average 'life expactancy' of an atom is.
We can say what the average life expectancy is, but the answer depends
on which average we talk about.
Echo the first part of this - although talk of different kinds of
averages usually strikes me as misleading. We're talking about
"average" and "expectancy" of a single unstable atom, I think.
The probability that a given particle will decay is calculated with the
same equations and constants that describe the rate of decay of a large
number of such particles. We can say that since Unobtanium-365 has a
half-life of 10 minutes, 10kg of Ub will become 5kG of Ub and ~5kg of
something else in ten minutes. This is, in the end, the same thing as
saying that I'll give you even odds that a given atom of Ub-365 will
still be here ten minutes from now, or odds of 1/4 that it will not have
decayed in 20 minutes. (Yep, and 30-minute futures on Ub-365 are down
88%).
We
certainly can put figures to those statistical estimates. We can't
predict the decay - and the point of putting it in the Schrodinger's
cat thought-experiment, I think, is that even inside the atom, the
process of decay isn't a definite event determined by classical
mechanics. But the average and the expectancy are matters of
probability and odds.
We can't predict the decay of any given atom, but we *can* predict the
way a bunch of particles of a given type will decay.
Half-lives are useful to characterize things other than radioactive
decay. The reactions given in http://www.tim-thompson.com/fusion.html ,
useful in answering a question in a different thread, are characterized
by the average time each particle can expect to remain in that state. A
more accurate time would be the half-life of those particles. It's not
the radioactive half-life, but the time in which half the particles have
undergone the next stage in the chain reaction.
That is, when p + p -> d + e+ + nu is given as 7.9E9 years, that does
not mean that a proton hangs out for eight billion years before joining
up with another one. It means that that's the average wait. Some small
fraction of the protons undergo that reaction much sooner.
One of the reasons that the sun doesn't create any particles heavier
than He is that the radioactive half-life of all particles of atomic
weight 8 is far, far shorter than their fusion-reaction half-lives would
be.
--
Timberwoof <me at timberwoof dot com> http://www.timberwoof.com
"When you post sewage, don't blame others for
emptying chamber pots in your direction." ?Chris L.
an important web site: http://www.muslim-refusenik.com/
.
- References:
- Halflife and Randomness
- From: alwaysaskingquestions
- Re: Halflife and Randomness
- From: Ernest Major
- Re: Halflife and Randomness
- From: Robert Carnegie
- Halflife and Randomness
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