Q105 / 180 · AIIMS 2005 · Physics

A radioactive material has a half-life of 10 days. What fraction of the material would remain after 30 days?

  • A
    0.5
  • B
    0.25
  • Correct answer
    C
    0.125
  • D
    0.33

Solution

$T_{1 / 2}=10$ days, $T=30$ days $$ \begin{aligned} & T=n \times T_{1 / 2} . \Rightarrow n=\frac{T}{T_{1 / 2}}=\frac{30}{10}=3 \\ & \frac{N}{N_0}=\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^3=\frac{1}{8}=0.125 . \end{aligned} $$

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

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