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NEET Sample Paper NEET Sample Test Paper-78

  • question_answer
    The radioactivity of a sample is \[{{I}_{1}}\] at a time \[{{t}_{1}}\] and \[{{I}_{2}}\] at a time\[{{t}_{2}}\]. If the half-life of the sample is \[{{\tau }_{1/2}}\] then the number of nuclei that have disintegrated in the time \[{{t}_{2}}-{{t}_{1}}\] is proportional to

    A)  \[{{l}_{1}}{{t}_{2}}-{{l}_{2}}{{t}_{1}}\]                  

    B)  \[{{l}_{1}}-{{l}_{2}}\]

    C)  \[\frac{{{l}_{1}}-{{l}_{2}}}{{{\tau }_{1/2}}}\]                       

    D)  \[\left( {{l}_{1}}-{{l}_{2}} \right)\,{{\tau }_{1/2}}\]

    Correct Answer: D

    Solution :

    Half-life \[{{\tau }_{1/2}}\,\,=\,\,\frac{0.693}{\lambda }\] Activity    \[{{I}_{1}}\,\,=\,\,\lambda {{N}_{1}},\,\,and\,\,{{I}_{2}}\,\,=\,\,\lambda {{N}_{2}}\] \[\lambda \,\,\to \,\, disintegration constant\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{l}_{1}}-{{l}_{2}}=({{N}_{1}}-{{N}_{2}})\frac{0.693}{{{\tau }_{1/2}}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,({{N}_{1}}-{{N}_{2}})\,\,\propto \,\,({{l}_{1}}-{{l}_{2}})\,{{\tau }_{1/2}}\]


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