Given 100.0 g of a radioactive isotope that has a half-life of 25 years, what amount of that isotope will remain after 100 years?

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Answer 1 · 2017-03-30T12:07:55

After 100 years, 6.25g will remain.

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We can follow the half-life formula to solve.

Following the image, we have the formula #A=A_o*(1/2)^(t/h)#

Now we'd plug in for each variable we have.

#A_o#, our initial amount, would be 100 grams.

Our #t#, time, would be 100 years.

Our #h#, the isotope's half-life, is 25 years.

We currently have #A=100*(1/2)^(100/25)#, which simplifies to
#A=100*(1/2)^4#

We can plug all that into a calculator, or solve for the exponent first. #(1/2)^4=.0625#.

#.0625*100=6.25#.

After 100 years, 6.25g will remain.