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

  • question_answer
    A radioactive nucleus a decays to a stable nucleus ?Y?. Then the graph of rate of formation of ?Y? against time ?t? will be  

    A)  

    B)  

    C)  

    D)  

    Correct Answer: C

    Solution :

    [c]  \[N={{N}_{0}}{{e}^{-\lambda t}}\Rightarrow {{N}_{y}}={{N}_{0}}(1-{{e}^{-\lambda t}})\] Rate of formation of \[Y=\frac{dN}{dt}=+\lambda {{N}_{0}}{{e}^{-\lambda t}}\] \[X\xrightarrow{{}}Y\] At \[t=0,\,\,\,\,\,\,\,R=\lambda {{N}_{0}}\Rightarrow t=0\,\,\,{{N}_{0}}\] \[t=\infty ,\,\,\,R=0\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,t=t\,\,\,\,\,\,\,\,\,N\] \[{{N}_{y}}={{N}_{0}}(1-{{e}^{-\lambda t}})\]


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