Re: Physics Question

From	Fabian Russell <fb@zen.info>
Newsgroups	sci.physics
Subject	Re: Physics Question
Date	2016-07-09 17:11 +0000
Organization	NewsGuy - Unlimited Usenet $23.95
Message-ID	<nlrb7q01882@news6.newsguy.com> (permalink)
References	<nllle2$1q3n$1@gioia.aioe.org> <nlnj6p$4h7$1@dont-email.me>

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On Fri, 08 Jul 2016 09:02:48 +0200, Poutnik wrote:

>
> Incomplete scenario definition without probabilities.
> 

Nonsense.  The correct answer is A: 30 minutes

The problem is perfectly valid and represents what a chemist
would call consecutive first-order reactions:

A --> B --> C

In this case, B is a metastable nucleus that will "decay"
to a stable nucleus by gamma emission.

If we let k1 be the rate constant for A --> B, and k2 be the
rate constant for B --> C, then:

dA/dt = -k1 * A

dB/dt = k1*A - k2 * B

dC/dt = k2 * B

Solving simultaneously we get:

C = A0 * ( 1 + 1/(k1-k2) * (k2*exp(-k1*t) - k1*exp(-k2*t)) ) 

Letting C = 1/2 * A0, that is the initial amount of A,
we can then solve for the half life knowing that: 

k1 = ln(2)/36 min

k2 = ln(2)/24 min

The final answer is 29.8826999480768 min = 30 min

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Physics Question Sergio <invalid@invalid.com> - 2016-07-07 08:28 -0500
  Re: Physics Question Poutnik <poutnik4nntp@gmail.com> - 2016-07-08 09:02 +0200
    Re: Physics Question Sergio <invalid@invalid.com> - 2016-07-08 09:19 -0500
    Re: Physics Question moroney@world.std.spaamtrap.com (Michael Moroney) - 2016-07-08 15:06 +0000
      Re: Physics Question Odd Bodkin <bodkinodd@gmail.com> - 2016-07-08 10:11 -0500
        Re: Physics Question benj <benj@nobody.net> - 2016-07-08 17:12 -0400
          Re: Physics Question Odd Bodkin <bodkinodd@gmail.com> - 2016-07-08 16:32 -0500
            Re: Physics Question Sergio <invalid@invalid.com> - 2016-07-10 11:15 -0500
              Re: Physics Question Fabian Russell <fb@zen.info> - 2016-07-10 19:25 +0000
                Re: Physics Question Odd Bodkin <bodkinodd@gmail.com> - 2016-07-10 15:43 -0500
                Re: Physics Question Fabian Russell <fb@zen.info> - 2016-07-10 21:52 +0000
                Re: Physics Question Odd Bodkin <bodkinodd@gmail.com> - 2016-07-11 07:50 -0500
                Re: Physics Question Poutnik <poutnik4nntp@gmail.com> - 2016-07-11 17:04 +0200
                Re: Physics Question moroney@world.std.spaamtrap.com (Michael Moroney) - 2016-07-11 01:20 +0000
      Re: Physics Question Poutnik <poutnik4nntp@gmail.com> - 2016-07-08 19:01 +0200
        Re: Physics Question Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-07-09 21:28 +0200
          Re: Physics Question moroney@world.std.spaamtrap.com (Michael Moroney) - 2016-07-10 02:18 +0000
    Re: Physics Question Fabian Russell <fb@zen.info> - 2016-07-09 17:11 +0000

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