# A2 Physics half life question

#### CaptainBlack

##### Well-known member

I've got some A2 physics homework and unfortunately i can't seem to do the first question :
The question is: 61Co has a half life of 100 minutes. how long will it take for the radioactive isotope to reduce to 80% of the initial value?

The answer is 32 minutes, but of course i'll need the workings before it to actually prove i can do the question.

Thank you for any help given! (if any is anyway).

The key idea is that after 100 minutes 1/2 remains after 200 minutes 1/4 remains so t
he fraction remaining after $$t$$ minutes is:

$Q=2^{-t/100}$

So if $$80\%$$ remains we need to solve:

$0.8=2^{-t/100}$

which we do by taking logs (the base is unimportant as long as we use the sane base throughout):

$\log(0.8)= -\; \frac{t}{100} \log(2)$

So:

$t=- \; \frac{\log(0.8)}{\log(2)} \times 100$