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The Nucleus — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThe Nucleus2 Marks
Question
The decay constant of $\text{ }^{197}_{80}\text{Hg} ($electron capture to $\text{ }^{197}_{79}\text{Au})$ is $1.8 \times 10^{-4} S^{-1}$.
  1. What is the half$-$life?
  2. What is the average$-$life?
  3. How much time will it take to convert $25\%$ of this isotope of mercury into gold?
✓

Answer

  1. $\text{t}_{\frac{1}{2}}=\frac{0.693}{\lambda} [\lambda\rightarrow$ Decay constant$]$
$\Rightarrow\text{t}_{\frac{1}{2}}=3820\text{sec}=64\text{min}$
  1. Average life $=\frac{\text{t}_{\frac{1}{2}}}{0.693}=92\text{min}.$
  2. $0.75=1\text{e}^{-\lambda\text{t}}\Rightarrow\text{In }0.75=-\lambda\text{t}$
$\Rightarrow\text{t}=\text{In}\frac{0.75}{-0.00018}=1598.23\text{sec.}$

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