MHT CET · Chemistry · Chemical Kinetics
A radioactive isotope having \(t_{1 / 2}=3\) days was read after 12 days. If \(3 g\) of isotope is contained in container, the initial weight of isotope was
- A \(12 \mathrm{~g}\)
- B \(24 \mathrm{~g}\)
- C \(36 \mathrm{~g}\)
- D \(48 \mathrm{~g}\)
Answer & Solution
Correct Answer
(D) \(48 \mathrm{~g}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} T &=n \times t_{1 / 2} \\ 12 &=n \times 3 \\ n &=4 \\ N &=N_{0} \times\left(\frac{1}{2}\right)^{n} \\ 3 &=N_{0} \times\left(\frac{1}{2}\right)^{4} \\ 3 &=N_{0} \times \frac{1}{16} \\ N_{0} &=16 \times 3=48 \mathrm{~g} \end{aligned}\)
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