Re: Nuclear rate of decay quandary

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Kismet Talaat wrote:

> Hello all. I'm hoping someone out there can point out the error in
> these two conflicting solutions to the same problem.
>
> The problem states that ...  "In a certain collection of nuclei there
> were initially 1024 nuclei and 20 minutes later there was only one
> nuclei left, the others having decayed. On the basis of this
> information, how many nuclei would you estimate decayed in the first
> six minutes?"
>
> Several solutions were presented by the students:
>
> 1. Using  Nf = No x 0.5^n (where n = # half lives), it was found that
> 10 halflives had passed for the sample to go from 1024 nuclei to one
> nuclei. This was used to solve for the half life being 2 minutes, and
> made the decay constant lambda = ln 2 / 120 seconds, or 5.78^-3/sec.
> This decay constant was used with the formula for rate change ... delta
> N = lambda *No * t .... (No = 1024, t = 360 seconds) and gave an
> answer for the estimate of the number of nuclei that decayed (delta N)
> in the first 6 minutes of 2129 nuclei that decay...more than the
> original sample population!

I think it should be dt (delta t) and not t in
... delta N = lambda * No * t ...