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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    The radioactivity of a sample is \[{{R}_{1}}\] at a time \[{{T}_{1}}\]and \[{{R}_{2}}\] at a time \[{{T}_{2}}\]. If the half-life of the specimen is \[T,\] the number of atoms that have disintegrated in the time \[({{T}_{2}}-{{T}_{1}})\] is proportional to

    A)  \[({{R}_{1}}{{T}_{1}}-{{R}_{2}}{{T}_{2}})\]            

    B)  \[({{R}_{1}}-{{R}_{2}})\]

    C)  \[({{R}_{1}}-{{R}_{2}})/T\]                          

    D)  \[({{R}_{1}}-{{R}_{2}})\,T\]

    Correct Answer: D

    Solution :

     \[{{R}_{1}}=\lambda {{N}_{1}},\] \[{{R}_{2}}=\lambda {{N}_{2}}\] Number of atoms decayed in\[({{T}_{1}}-{{T}_{2}})\]. \[{{N}_{1}}-{{N}_{2}}=\frac{{{R}_{1}}-{{R}_{2}}}{\lambda }\] \[=\frac{({{R}_{1}}-{{R}_{2}})T}{\theta .693}\] \[{{N}_{1}}-{{N}_{2}}\propto ({{R}_{1}}-{{R}_{2}})T\]


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