J & K CET Medical J & K - CET Medical 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\[2\times {{10}^{6}}\] dpm. What is the average life (in min) of this nuclide?

    A)  100                                       

    B)  10

    C)  1                                            

    D)  0.1

    Correct Answer: B

    Solution :

                    \[k=\frac{2.303}{t}\log \frac{{{N}_{0}}}{N}\] \[=\frac{2.303}{23.03}\log \frac{2\times {{10}^{7}}}{2\times {{10}^{6}}}\]                 \[=\frac{2.303}{23.03}\log 10\] \[k=0.1\text{ }mi{{n}^{-1}}\]                 \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{0.1}=0.93\,\min \] average life \[(T)=1.44\times {{t}_{1/2}}\] \[=1.44\times 6.93=10\text{ }min\]


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