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..
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