Estimating activity of a radiocative sample

[shannon.leigh]

Homework Statement

A sample of processed waste from a nuclear reactor contains 1.0*10^24 plutonium-239 atoms. The half life of plutonium-239 is 2.41*10^4 years.
a) How many plutonium-239 atoms will decay in the next 2.41*10^4 years?
b) Estimate the activity of the original sample.

Homework Equations

I guess that A=Ao(1/2)^t/(t*o.5)nwould be relevant, but really I don't see how. A= the decaying quantity remaining, which I know anyway, and nothing else that I could rearrange the equation for will tell me the right answer.

The Attempt at a Solution

I managed to do a) alright, but I can't figure out b).
I can't really attempt the solution because I have no idea how. I know that the activity will be divided by 2 after each half life, but I don't know how to estimate the current activity to find the original. Please help me!

Thank you

 

[fearTheEcma]

The activity is related to the half-life. Activity (A) = $$\lambda$$ N. $$\lambda$$ is the decay constant of the element and N is the number of atoms in the sample. Half-life (H) = ln(2)/$$\lambda$$. With this, you should be able to rewrite activity in terms of given quantities.

 

[shannon.leigh]

Thankyou for that!. . .but I still have one question. . .What's the decay constant? As In how do you calculate it? I think I've been learning by different names. . .

 

[fearTheEcma]

The decay constant crops up in exponential decay problems in all sorts of different equations.

It is in the defining equation of exponential decay $$\frac{dN}{dt}=\lambda N$$. The solution to this equation is often written $$N=N_0 e^{\lambda t}$$.

You may see it most often in its inverse form as $$\tau=1/\lambda$$.

With this relation, it is easy to derive the equation for half-life.

The decay constant is inversely proportional to the half-life. Half-life=ln(2)/$$\lambda$$. If you rearrange that equation, you should be able to find $$\lambda$$ in terms of a known quantity in this problem, the half-life.

This is the way to calculate $$\lambda$$ for this problem, but please do not memorize just that method. There are lots of ways of calculating $$\lambda$$. Generally, you will have to look at the equations that you know, find the parameters that you know, and then rearrange those equations to find the parameters that you need.