A radioactive isotope has a half-life of 9 hours. How do you find the amount of the isotope left from a 80-milligram sample after 54 hours?

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Answer 1 · 2015-12-30T09:46:48

After 54 hours, 1.25 milligrams of the sample will be left.

After a half-life period, the quantity of the sample with be reduced to half.

So, after 9 hours, amount of sample left
#=80 * 1/2 = 40# milligrams

After another 9 hours, amount of sample left
#=40*1/2#
or, #80*1/2*1/2=80*(1/2)^2=20# milligrams

Do you see the pattern emerging?

In 54 hours, there are #54/9 = 6# half-life periods.

Therefore, amount of sample left after 54 hours
= amount of sample left after 6 half-life periods

#= 80 *(1/2)^6=80/64=1.25# milligrams