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?

1 Answer
Tanish J.
Dec 30, 2015

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

Explanation:

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=80⋅12=40 milligrams

After another 9 hours, amount of sample left
=40*1/2=40⋅12
or, 80*1/2*1/2=80*(1/2)^2=2080⋅12⋅12=80⋅(12)2=20 milligrams

Do you see the pattern emerging?

In 54 hours, there are 54/9 = 6549=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=80⋅(12)6=8064=1.25 milligrams

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