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JIPMER 2009
Exam
JIPMER
Year
2009
Subject
Chemistry
Chapter
Chemical Kinetics

JIPMER 2009 · Chemistry · Chemical Kinetics

If 50 \% of a radioactive substance dissociates in 15 min , then...

If 50%50 \% of a radioactive substance dissociates in 15 min , then the time taken by substance to dissociate 99%99 \% will be

Options

  1. A50 min
  2. B100 min
  3. C99 min
  4. D150 min

Correct answer

C. 99 min

Step-by-step solution

Radioactive disintegration is a Ist order reaction, hence k=2.303tlog⁡aa−x∴k=2.30315log⁡100100−50 also k=2.303tlog⁡100100−99∴2.30315log⁡10050=2.303tlog⁡1001115log⁡2=1tlog⁡1000.301015=2tt=2×150.3010=99min\begin{aligned} k & =\frac{2.303}{t} \log \frac{a}{a-x} \\ \therefore \quad k & =\frac{2.303}{15} \log \frac{100}{100-50} \\ \text{ also } \quad k & =\frac{2.303}{t} \log \frac{100}{100-99} \\ \therefore \frac{2.303}{15} \log \frac{100}{50} & =\frac{2.303}{t} \log \frac{100}{1} \\ \frac{1}{15} \log 2 & =\frac{1}{t} \log 100 \\ \frac{0.3010}{15} & =\frac{2}{t} \\ t & =\frac{2 \times 15}{0.3010}=99 \mathrm{ min} \end{aligned}
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