If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?

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- Jun 14th 2009, 04:02 PMNevershRadioactive Decay
If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?

- Jun 14th 2009, 04:22 PMJhevon
we use the formula $\displaystyle A(t) = A_0e^{-rt}$

where $\displaystyle A(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle A_0$ is the initial amount, and $\displaystyle r$ is the decay constant.

say $\displaystyle A_0 = 1$, then when $\displaystyle t = 250$, we have

$\displaystyle 0.8 = e^{-250r}$

use that equation to find $\displaystyle r$.

after that, you can answer the other questions (the half-life is easy, it is $\displaystyle \frac {\ln 2}r$)