Equilibrium between release and decay Kr-85

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SUMMARY

The discussion centers on calculating the mass of Kr-85 in the atmosphere when a power plant releases 2.0 grams daily, achieving equilibrium with its decay rate. The decay constant (λ) is crucial for this calculation, as it relates the activity (A) to the number of atoms (N) present. The half-life of Kr-85 is 10.8 years, which is essential for determining the decay constant. The key equation derived is A/k = N, where A represents the decay rate, and k is the decay constant.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with the decay constant (λ) and its application
  • Knowledge of the relationship between activity (A) and the number of atoms (N)
  • Basic algebra for manipulating exponential decay equations
NEXT STEPS
  • Calculate the decay constant (k) for Kr-85 using its half-life of 10.8 years
  • Convert grams of Kr-85 to the number of atoms (N) for decay calculations
  • Explore the implications of continuous versus instantaneous release of radioactive materials
  • Study the principles of equilibrium in radioactive decay systems
USEFUL FOR

Students in nuclear physics, environmental scientists, and professionals in power plant operations who need to understand the dynamics of radioactive decay and its environmental impact.

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 \lambda 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 \lambda 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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