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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 17

  • question_answer
    The activity of a freshly prepared radioactive sample is \[{{10}^{10}}\] disintegrations per second, whose mean life is \[{{10}^{9}}s\]. The mass of an atom of this radioisotope is \[{{10}^{-25}}kg\]. The mass (in mg) of the radioactive sample is

    A) 1         

    B)        3       

    C) 5         

    D)        6

    Correct Answer: A

    Solution :

    We know that, \[\left| \frac{dN}{dt} \right|=\lambda N=\frac{1}{{{T}_{mean}}}N\] \[\therefore \,\,\,{{10}^{10}}=\frac{1}{{{10}^{9}}}\times N\] \[\therefore \,\,N={{10}^{19}}\] i.e., \[{{10}^{19}}\] radioactive atoms are present in the freshly prepared sample. The mass of the sample \[\therefore \,\,={{10}^{19}}\times {{10}^{-25}}kg={{10}^{-6}}kg=1mg\]


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