if the half-life of a unstable isotope is 10,00 years and only 1/8 of the radioactive parent remains how old is the sample?
10,000
20,000
30,000 or
40,000

Question

if the half-life of a unstable isotope is 10,00 years and only 1/8 of the radioactive parent remains how old is the sample? 
10,000
20,000 
30,000 or 
40,000

thomaster · Answer

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The half life is 10,000 years i assume?
This is the time when $\frac{1}{2}$ of the isotopes is left.
After 2 half lifes there is $\frac{1}{2}*\frac{1}{2}=\frac{1}{4}$ left
After 3 half lifes there is $\frac{1}{4}*\frac{1}{2}=\frac{1}{8}$ left

There is $\frac{1}{8}$ left after 3 half lifes, which is 3 times 10,000 years.
So the answer is 30,000 years :D

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