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?

Rigoberto Drake

Rigoberto Drake

Answered question

2022-11-03

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?

Answer & Explanation

Cindy Mercer

Cindy Mercer

Beginner2022-11-04Added 13 answers

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

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