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.