1. Tardigrade
  2. Question
  3. Physics
  4. The initial activity of a certain radioactive isotope was measured as 16000 counts min -1. Given that the only activity measured was due to this isotope and that its activity after 12 h was 2100 counts min -1, its half-life, in hours, is nearest to [Given log e(7.2)=2 ]

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Q. The initial activity of a certain radioactive isotope was measured as $16000$ counts $\min ^{-1}$. Given that the only activity measured was due to this isotope and that its activity after $12\, h$ was $2100$ counts $min ^{-1}$, its half-life, in hours, is nearest to [Given $\log _{e}(7.2)=2$ ]

Nuclei

Solution:

$A=A_{0} e^{-\lambda t} ; 2100=16000\, e^{-12 \lambda}$
$\Rightarrow e^{12 \lambda}=7.6$
$\Rightarrow 12 \lambda=\log _{e} 7.6=2$
$\Rightarrow \lambda=\frac{2}{12}=\frac{1}{6}$
$\therefore T=\frac{0.6931 \times 6}{1}=4$