Equilibrium between release and decay Kr-85

[Minkowski]

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

 

[Astronuc]

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.

 

[Minkowski]

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

 

[Astronuc]

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 N_d decaying, and the mean activity A (decay rate) is simply N_d/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.