NEET Sample Paper NEET Sample Test Paper-20

  • question_answer
    A radioactive substance is being produced at a constant rate 200 nuclei/s. The decay constant of the substance is \[1{{s}^{-1}}.\]After what time, the number of radioactive nuclei will become 100? Initially there are no nuclei present.

    A) \[1\,s\]                         

    B) \[\frac{1}{\ell n\,2}s\] 

    C)      \[(\ell n\,2)s\]   

    D)       2 s  

    Correct Answer: C

    Solution :

    \[\frac{dN}{dt}=200-\lambda N=200-N\] \[\Rightarrow \]\[\int_{0}^{N}{\frac{dN}{200-N}=\int_{0}^{t}{dt}}\] \[\therefore \]\[t=\ell n\left( \frac{200}{200-N} \right)=\ell n\left( \frac{200}{200-100} \right)=(\ell n2)\sec \] Hence, the correction option is (c).


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