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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Critical Thinking

  • question_answer
    A small quantity of solution containing Na24 radio nuclide of activity 1 microcurie is injected into the blood of a person. A sample of the blood of volume 1 cm3 taken after 5 hours shows an activity of 296 disintegration per minute. What will be the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person (Take 1 curie = 3.7 ´ 1010 disintegration per second and \[{{e}^{-\lambda t}}=0.7927;\] where l = disintegration constant)

    A)            5.94 litre                                 

    B)            2 litre

    C)            317 litre                                  

    D)            1 litre

    Correct Answer: A

    Solution :

               R0 = Initial activity = 1 micro curie = 3.7 ´ 104 d ps r = Activity in 1 cm3 of blood at t = 5 hrs \[=\frac{296}{60}dps=4.93\,dps\] R = Activity of whole blood at time t = 5 hr, Total volume should be \[V=\frac{R}{r}=\frac{{{R}_{0}}{{e}^{-\lambda t}}}{r}\] \[=\frac{3.7\times {{10}^{4}}\times 0.7927}{4.93}\]= 5.94 ´ 103 cm3  = 5.94 Litre.


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