[Phys-L] Re: Bateman (was survey meters)

[kowalskil at MAIL.MONTCLAIR.EDU (Ludwik Kowalski)]

CORRECTING MY LAST MESSAGE:
In the example given (To=100 years) the decay of #5, after going over
the maximum, follows the 100 y half-life only when its own half-life is
much smaller than To.

> Batemen equations, to which Bernard refers (see below), can be
> simplified when one is not interested in radioactivity associated with
> predecessors whose half-lives are relatively short. Consider this
> sequence:
>
> 0 --> 1 --> 2 --> 3 --> 4 --> 5 --> 6 --> 7 --> 8 -->
>
> where numbers refer to generations of isotopes. Suppose we are
> interested in the time dependence of radioactivity from the product #5
> when the initial activity, and the half-life To of the starter, are
> given. Initial amount of products #1, 2, 3 and 4 must be zeros in this
> formalism, as indicated by Bernard.
>
> Suppose that To=100 years while T1, T2, T3 and T4 are much shorter. In
> such case, to a very good approximation, one can say that the result is
> essentially the same as for a much easier case:
>
> 0 --> 5 --> 6
>
> The starter, as always, decays exponentially. The #5 grows accordingly
> and then decays exponentially at the same rate as the original.  This
> particular problem does not ask about radioactivity from #6, 7, 8, etc.
> The half-life of #5 is presumably given, for example, 200 minutes or
> 200 years.

Ludwik Kowalski
Let the perfect not be the enemy of the good.