Q39 / 180 · AIIMS 2007 · Chemistry

Decay constant of a radioactive substance is \(69.3 \mathrm{~sec}^{-1}\), find \(t_{1 / 16}\) of the same substance.

  • Correct answer
    A
    \(4 \times 10^{-2} \mathrm{~sec}\)
  • B
    \(2 \times 10^{-2} \mathrm{~sec}\)
  • C
    \(1 \times 10^{-2} \mathrm{~sec}\)
  • D
    None of these

Solution

\(1 \stackrel{t_{1 / 2}}{\longrightarrow} \frac{1}{2} \stackrel{t_{1 / 2}}{\longrightarrow} \frac{1}{4} \stackrel{t_{1 / 2}}{\longrightarrow} \frac{1}{8} \stackrel{t_{1 / 2}}{\longrightarrow} \frac{1}{16}\) So, \(t_{1 / 16}=4 t_{1 / 2}\) \(=4 \times \frac{0.693}{\lambda}=4 \times \frac{0.693}{69.3}=4 \times 10^{-2} \mathrm{sec} .\)

Hence, the correct answer is option: 'A'.

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