# Thread: Half-life problem. Please help :)

1. ## Half-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..

2. Originally Posted by c47v3770
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..
How many half lives does 1500 years represent .....?

By the way, your question has nothing to do with advanced probability and statistics and so is not appropriate for this forum.

3. Originally Posted by c47v3770
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..
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