Q93 / 160 · JIPMER 2004 · Physics

The half life of a radioactive substance is 3.6 days. How much of 20 mg of this radioactive substance will remain after 36 days?

  • A
    0.0019 mg
  • B
    1.019 mg
  • C
    1.109 mg
  • Correct answer
    D
    0.019 mg

Solution

Half life $T_{1 / 2}=3.6$ days Initial quantity $N_0=20 \mathrm{mg}$ Total time $=36$ days The number of half lives $n=\frac{t}{T_{1 / 2}}=\frac{36}{3.6}=10$ Hence, mass of radioactive substance left after 10 half lives $N=N_0 \times\left(\frac{1}{2}\right)^n=20 \times \frac{1}{1024}=0.019 \mathrm{mg}$

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

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