A containing active cobalt ⁶⁰₂₇Co having activity of 0.8 and decay… | JEE Main 2018 (15 Apr, Shift 1)

Q87JEE Main 2018 · 15 APR · SHIFT 1Difficult

Law of Radioactive Decay

A containing active cobalt ${}^{60}_{27}\text{Co}$ having activity of $0.8\ \mu\text{Ci}$ and decay constant $\lambda$ is injected in an animal's body. If $1\text{ cm}^3$ of blood is drawn from the animal's body after $10$ hrs of injection, the activity found was $300$ decays per minute What is the volume of blood that is flowing in the body? $(\text{Ci} = 3.7 \times 10^{10}$ decays per second and at $t = 10$ hrs $e^{-\lambda t} = 0.84)$

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Answer: (d)

Initial activity: $0.8 \times 10^{-6} \times 3.7 \times 10^{10} = 2.96 \times 10^{4}$ decays/s.
After 10 h: $2.96 \times 10^{4} \times 0.84 \approx 2.49 \times 10^{4}$ decays/s in the whole blood.
Activity of $1\text{ cm}^3$ : $\dfrac{300}{60} = 5$ decays/s.
$V = \dfrac{2.49 \times 10^{4}}{5} \approx 4973\text{ cm}^3 \approx 5$ liters
So the answer is (d) 5 liters.

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Law of Radioactive Decay question from JEE Main 2018 (15 Apr, Shift 1)

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