Iodine-123 is a radioactive substance used in medicine. It has a half-life of 13 hours. A nurse received a solution that initially contained 48 grams of iodine-123. Now only 12 grams of the iodine-123 remain. How many hours have passed since the nurse received the solution?

Question

Mathematics

Shrinkwrap

3 April, 12:37

Iodine-123 is a radioactive substance used in medicine. It has a half-life of 13 hours. A nurse received a solution that initially contained 48 grams of iodine-123. Now only 12 grams of the iodine-123 remain. How many hours have passed since the nurse received the solution?

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Answers (1)

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Ariana Hooper · Answer 1

Ok

A=P (1/2) ^ (t/h)

A=amount final

P=initial amount

t=time elapsed

h=time of half life

so

given h=13

and initial = 48g

and final is 12g

12=48 (1/2) ^ (t/13)

divide both sides by 48

1/4 = (1/2) ^ (t/13)

what a coincidence

(1/2) ^2 = (1/2) ^ (t/13)

so

2=t/13

26=t

26 hours have passed