Radioactive Decay

**Neversh** · June 14th 2009, 04:02 PM

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?

**Jhevon** · June 14th 2009, 04:22 PM

Originally Posted by Neversh

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?

we use the formula $A(t) = A_0e^{-rt}$

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

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

$0.8 = e^{-250r}$

use that equation to find $r$ .

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

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