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A radio active cobalt used for cancer chemotherapy having half life 3 hrs. It was sent to a hospital which is received after 12 hrs. At the time of receiving it was left only 3 gms. What was the initial amount (in grams) ___________.
Correct Answer: 48
12 hours is $$\frac{12}{3} = 4$$ half-lives, so the amount falls to $$\left(\frac{1}{2}\right)^4 = \frac{1}{16}$$ of the initial value. The initial amount was $$3 \times 16 = 48\text{ g}$$.
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