Guys, could you please help me with this problem?

"The half-life of a radioactive substance is 250 years. What fraction of a certain amount of the substance will remain after 1500 years?"

Is there a formula I need to use?

Thanks a bunch..

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- Aug 6th 2008, 07:50 PMc47v3770Half-life problem. Please help :)
Guys, could you please help me with this problem?

"The half-life of a radioactive substance is 250 years. What fraction of a certain amount of the substance will remain after 1500 years?"

Is there a formula I need to use?

Thanks a bunch.. - Aug 6th 2008, 07:56 PMmr fantastic
- Aug 6th 2008, 08:01 PMChris L T521
The formula for radioactive decay is $\displaystyle N=N_0e^{-kt}$, where $\displaystyle N_0$ is the initial amount of a substance, $\displaystyle N$ is the amount of a substance after t years, and $\displaystyle k$ is the decay constant.

The decay constant can be found using the half life formula $\displaystyle \lambda=\frac{\ln(2)}{k}$

So we see that $\displaystyle k=\frac{\ln2}{\lambda}=\frac{\ln2}{250}$

Thus, our equation would be $\displaystyle N=N_0e^{-\frac{\ln2}{250}t}$

After 1500 years, we have $\displaystyle N=N_0e^{-\frac{\ln2}{250}1500}\implies N=N_0e^{-6\ln(2)}\implies N=\tfrac{1}{64}N_0$

Thus, the amount of substance remaining after 1500 years will be $\displaystyle \tfrac{1}{64}$ of the original substance.

Does this make sense? If you have a question, feel free to ask. We're here to help you.

--Chris