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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    Two identical samples (same material and same amount) P and Q of a radioactive substances 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 ages 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) \[t\left( \frac{{{A}_{P}}}{{{A}_{Q}}} \right)\]

    Correct Answer: B

    Solution :

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


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