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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Self Evaluation Test - Nuclei

  • question_answer
    A radioactive substance with decay constant of \[0.5{{s}^{-1}}\] is being produced at a constant rate of 50 nuclei per second. If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is

    A)  1        

    B)                     In 2  

    C)  In (4/3)            

    D)         2 to (4/3)

    Correct Answer: D

    Solution :

    [d] \[\frac{dN}{dt}=50-\frac{N}{0.5}\,\,\,\,\,\,\,\,\,\int\limits_{0}^{N}{\frac{dN}{50-2N}}=\int\limits_{0}^{t}{dt}\] \[N=(100(1-{{e}^{-t/2)}})=25\] \[t=2\]   In \[(4/3)\]  


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