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COMEDK · Chemistry · 19. Chemical Kinetics

A radioactive isotope decays at such a rate that after 192 minutes only \(\frac{1}{16}\) of the original amount remains. The half-life of the radioactive isotope is

  1. A \(12 \mathrm{~min}\)
  2. B \(24 \mathrm{~min}\)
  3. C \(32 \mathrm{~min}\)
  4. D \(48 \mathrm{~min}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(48 \mathrm{~min}\)

Step-by-step Solution

Detailed explanation

For radioactive decay \(t_{1 / 2}=\frac{0.693}{k}\) For concentration to reduce to \(\frac{1}{16}\) of original amount \(\begin{aligned} t &=t_{1 / 2} \times 4 \\ \therefore \quad t_{1 / 2} &=\frac{192}{4}=48 \mathrm{~min} \end{aligned}\)