I need a refresher on calculus need to derive this equation, the question is:(adsbygoogle = window.adsbygoogle || []).push({});

A --> B --> C

and where decay constants:

http://img183.imageshack.us/img183/4403/aki2.jpg [Broken]

Derive an expression for the activity of B as a function of time.

So what I'm having trouble with is changing the derivation for the number of N when lambda_A = lambda_B so that I derive the activity of B.

Normally we would have:

http://img157.imageshack.us/img157/3501/ajh6.jpg [Broken]

But because of the condition, we have to go about it differently. So setting the decay constants equal to each other:

http://img182.imageshack.us/img182/192/asa5.jpg [Broken]

And this is where I get a little stumped trying to change the derivation. When lambda_A doesn't equal lambda_B, the derivation ends up with:

http://img226.imageshack.us/img226/1602/akk1.jpg [Broken]

The problem I'm having is that I'm not sure what has to be done differently in the original derivation to solve for activity, my calculus skills are a little rusty so if anyone has any suggestions or advice, it's greatly appreciated.

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# Homework Help: Radioactive decay equilibrium when decay constants are equal

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