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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Chemistry
Chapter
Chemical Kinetics

BITSAT 2020 · Chemistry · Chemical Kinetics

A radioactive isotope having a half - life period of 3 days was...

A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g3 \mathrm{ g} of the isotope is left in the container, what would be the initial mass of the isotope?

Options

  1. A12g12 \mathrm{ g}
  2. B36g36 \mathrm{ g}
  3. C48g48 \mathrm{ g}
  4. D24g24 \mathrm{ g}

Correct answer

C. 48g48 \mathrm{ g}

Step-by-step solution

Given t1/2=3t_{1/2}=3 Total time T=12\mathrm{T}=12 No. of half lives (n)=123=4(12)n=NNo∴(12)4=3N3N=116N=48(n)=\frac{12}{3}=4\left(\frac{1}{2}\right)^{n}=\frac{\mathrm{N}}{\mathrm{N}_{\mathrm{o}}} \therefore\left(\frac{1}{2}\right)^{4}=\frac{3}{\mathrm{ N}}\frac{3}{\mathrm{ N}}=\frac{1}{16}N=48
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