Lamarsh Assignment: Discover the 7-10 Rule for Fission Product Activity

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Discussion Overview

The discussion revolves around the 7-10 rule for fission product activity, specifically how to demonstrate that the activity at time t=7^nt0 is approximately a=a0/10^n. The scope includes mathematical reasoning and conceptual understanding related to nuclear decay and civil defense applications.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant presents the initial problem statement regarding the 7-10 rule and its relation to fission product activity.
  • Another participant inquires about the equations available for analysis and connects the problem to the exponential decay formula a(t) = a0 * exp(-0.693 t/t1/2).
  • A different participant discusses their exploration of exponential decay and expresses uncertainty about the variable n, questioning whether it represents the number of atoms or is an arbitrary variable.
  • One participant notes the approximation of 0.693 to 0.7 and discusses the difference between continuous decay functions and the discrete time intervals used in the rule of thumb, providing an example of activity reduction over specified time intervals.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and uncertainty regarding the application of the 7-10 rule and the relevant equations. No consensus is reached on the interpretation of the variable n or the best approach to demonstrate the rule.

Contextual Notes

There are limitations regarding the assumptions about the variable n and its definition, as well as the dependence on the choice of time intervals for applying the rule. The discussion does not resolve these uncertainties.

psunuce
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Fission product activity measured at the time t0 following the burst of a nuclear weapon is found to be a0. Show that the activity at the time t=7^nt0 is given approximately by a=a0/10^n. This is known as the 7-10 rule in civil defense.
 
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What equations do you have to work with?

How does it relate to a(t) = a0* exp(-0.693 t/t1/2)?
 
Yes, I was playing around with that one... Exponential decay for activity... I'm not sure what else I can use... At one point, I also used n = n0 *exp (-0.693t/t12), but wasn't sure if the n given in the problem was actually number of atoms or just some arbitrary variable.
 
I noticed that 0.693 is approximately 0.7 or 7/10.

The decaying exponential is a continuous function, and the rule of thumb uses discrete interval of time.

So one could pick a [itex]\Delta{T}[/itex] of one hour or one day.

According to an example, if activity is measured at 1 hr, then 8 hrs ([itex]\Delta{T}[/itex] = 7 hrs), activity should be reduced to 1/10 of the activity at 1 hr. Then at 15 hrs, 1 + 2*7, the activity should be 1/100 of the activity at 1 hr. And so on.
 
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