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NEET Sample Paper NEET Sample Test Paper-66

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

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

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

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

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

    Correct Answer: C

    Solution :

    \[{{A}_{1}}={{N}_{1}}\lambda ,\,\,\,\,\,\,\,\,\,\,{{A}_{2}}={{N}_{2}}\lambda \] \[Mean\,\,life,\,\,T=\frac{1}{\lambda }\] \[{{A}_{1}}-{{A}_{2}}=({{N}_{1}}-{{N}_{2}})\,\lambda \,=\,({{N}_{1}}-{{N}_{2}})\,\frac{1}{T}\] So, number of atoms disintegrated in \[({{t}_{2}}-{{t}_{1}})\,sec=({{N}_{1}}-{{N}_{2}})=({{A}_{1}}-{{A}_{2}})T\]


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