Equilibrium between release and decay Kr-85

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Homework Help Overview

The problem involves the equilibrium between the release and decay of Kr-85 in the atmosphere, specifically focusing on the mass of Kr-85 that would result in a decay rate equal to the daily release of 2.0 grams by a power plant.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the decay constant and the activity of Kr-85, questioning whether the release is instantaneous or continuous. There is mention of the half-life of Kr-85 and the need to find a mass that allows for a decay rate of 2 grams per day.

Discussion Status

Some participants have provided insights into the relationship between activity and the number of atoms present, suggesting that the average activity can be converted to the number of decaying atoms. There is an ongoing exploration of the relevant equations and concepts, but no consensus has been reached on a specific method or solution.

Contextual Notes

Participants note the lack of explicit information regarding whether the release of Kr-85 is instantaneous or continuous, which may affect the calculations. The original poster expresses uncertainty about the appropriate equations to use given the nature of the decay function.

Minkowski
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Homework Statement



A power plant releases 2,0 grams of Kr-85 into the atmosphere every day. At some point there's an equilibrium between what the power plant releases into the atmosphere and the decay in the atmosphere -> The decay in atmosphere is equal to 2,0 grams per day

Calculate the mass of Kr-85 in the atmosphere for this to be possible


Homework Equations



I do not have any. Maybe: N = N0*e^-k*t but I am not sure

The Attempt at a Solution



I can't find a solution to this problem at all.

Thank you very much on beforehand!

/Thomas
 
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k is the decay constant, but [itex]\lambda[/itex] is conventionally used.

So in equilibrium, the production rate matches the decay rate.


The activity (A) is proportional to the number of atoms (N) present by k.

One is actually looking for the mean activity and mean mass, since the problem doesn't state if the release is instantaneous (i.e. a puff) or if it is continuous.
 
Astronuc said:
k is the decay constant, but [itex]\lambda[/itex] is conventionally used.

So in equilibrium, the production rate matches the decay rate.


The activity (A) is proportional to the number of atoms (N) present by k.

One is actually looking for the mean activity and mean mass, since the problem doesn't state if the release is instantaneous (i.e. a puff) or if it is continuous.

It is a continuous stream/release

I thought this: I know that the half-life is 10,8 years. I need to find a mass that enables the Kr-85 decay to release 2 grams/day. There must be an equation since it's impossible for me to calculate it since the half-life is an eks. function.

I know the formula and what it means, but I am not sure wheter it is the right one to use, and if I've got the rigt infos. to just plot them into the equation.?

Thanks a lot for for your help.
best regards
/Thomas
 
The decay in atmosphere is equal to 2,0 grams per day
That is an average activity, so convert 2.0 grams to number of atoms Nd decaying, and the mean activity A (decay rate) is simply Nd/time.

Then A/k = N, where k is the decay constant and N is the number of atoms present for that decay rate.

See where that takes one.
 

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