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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    The activity of a radioactive nuclide is \[2\times {{10}^{7}}\] disintegrations per minute (dpm). After 23.03 min, its activity is reduced to\[2\times {{10}^{6}}\text{ dpm}\text{.}\] What is the average life (in min) of this nuclide?

    A)  100          

    B)  10

    C)  1             

    D)  0.1

    Correct Answer: B

    Solution :

     \[k=\frac{2.303}{t}\log \frac{{{N}_{0}}}{N}\] \[=\frac{2.303}{23.03}\log \frac{2\times {{10}^{7}}}{2\times {{10}^{6}}}\] \[=\frac{2.303}{23.03}\log \,10\] \[k=0.1\,{{\min }^{-1}}\] \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{0.1}=6.93\,\min \] Average life \[(T)=1.144\times {{t}_{1/2}}\] \[=1.44\times 6.93=10\,\min \]


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