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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Nuclear Physics

JIPMER 2015 · Physics · Nuclear Physics

The half-life of ^ 198 Au is 2.7 days. The average life is

The half-life of 198Au{ }^{198} \mathrm{Au} is 2.7 days. The average life is

Options

  1. A4 days
  2. B3.4 days
  3. C3.9 days
  4. DNone of the above

Correct answer

C. 3.9 days

Step-by-step solution

The half-life and the decay constant are related as t12=ln⁡2λ=0.693λ⇒λ=0.693t1/2=0.6932.7day=0.6932.7×24×3600 s=2.9×10−6 s−1\begin{aligned} t_{12} & =\frac{\ln 2}{\lambda}=\frac{0.693}{\lambda} \\ \Rightarrow \quad \lambda & =\frac{0.693}{t_{1/2}}=\frac{0.693}{2.7 \mathrm{day}} \\ & =\frac{0.693}{2.7 \times 24 \times 3600 \mathrm{~s}} \\ & =2.9 \times 10^{-6} \mathrm{~s}^{-1}\end{aligned} Now average life tav=1λ=3.9t_{a v}=\frac{1}{\lambda}=3.9 days
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