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KVPY Sample Paper KVPY Stream-SX Model Paper-9

  • question_answer
    Two identical samples (same material and same amount) P and Q of a radioactive substance having mean life T are observed to have activities \[{{A}_{P}}\] & \[{{A}_{Q}}\] respectively at the time of observation. If P is older than Q, then the difference in their ager is:

    A) \[T\,\ell n\,\,\left( \frac{{{A}_{P}}}{{{A}_{Q}}} \right)\]             

    B) \[T\,\ell n\,\,\left( \frac{{{A}_{Q}}}{{{A}_{P}}} \right)\]

    C) \[\frac{1}{T}\,\ell n\,\,\left( \frac{{{A}_{P}}}{{{A}_{Q}}} \right)\]          

    D) \[T\,\,\left( \frac{{{A}_{Q}}}{{{A}_{P}}} \right)\]

    Correct Answer: B

    Solution :

    \[{{A}_{P}}={{A}_{Q}}\,{{e}^{-\lambda t}}={{A}_{Q}}\,{{e}^{-\,\frac{1}{T}\,t}}\]            \[\therefore \]      \[t=T\ell n\frac{{{A}_{Q}}}{A{{ & }_{P}}}\]


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