Q101 / 150 · MHT CET 2022 (11 Aug Shift 1) · Physics

Activity of a radioactive sample decreases to $\left(\frac{1}{3}\right)^{r d}$ of its original value in 3 days. Then in 9 days its activity reduces to

  • A
    $\left(\frac{1}{18}\right)$ of the original value
  • B
    $\left(\frac{1}{9}\right)$ of the original value
  • Correct answer
    C
    $\left(\frac{1}{27}\right)$ of the original value
  • D
    $\left(\frac{1}{3}\right)$ of the original value

Solution

Activity after time $t$ given that half-life is $T$ : $A=\frac{A_0}{2^{t / T}}$ $\frac{A_0}{3}=\frac{A_0}{2^{3 / T}}$ Activity in 9 days, $A=\frac{A_0}{2^{t / T}}=\frac{A_0}{2^{9 / T}}=\frac{A_0}{\left(2^{3 / T}\right)^3}=\frac{A_0}{27}$

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

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