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NEET Physics Nuclear Physics And Radioactivity NEET PYQ-Nuclear Physics

  • question_answer
    The half-life of a radioactive nucleus is 50 days. The time interval \[({{t}_{2}}-{{t}_{1}})\] between the time t2 when \[\frac{2}{3}\] of it has decayed and the time \[{{t}_{1}}\] when \[\frac{1}{3}\] of it had decayed is                                                                                                                           [AIPMT (M) 2012]

    A)  30 days           

    B)       50 days                                                            

    C)  60 days    

    D)  15 days

    Correct Answer: B

    Solution :

    Active fraction at instant \[{{t}_{2}},\]
       \[\frac{1}{{{2}^{{{t}_{2}}/{{T}_{1/2}}}}}=\frac{1}{3}\]
    Active fraction at instant \[{{t}_{1}},\]
    \[\frac{1}{{{2}^{{{t}_{1}}/{{T}_{1/2}}}}}=\frac{2}{3}\]
    \[\frac{{{2}^{{{t}_{2}}/{{T}_{1/2}}}}}{{{2}^{{{t}_{1}}/{{T}_{1/2}}}}}=2\]
    \[{{\frac{^{{{t}_{2}}-{{t}_{1}}}}{{{_{2}}^{{{T}_{1/2}}}}}}_{=2}}\]
                \[{{t}_{2}}-{{t}_{1}}={{T}_{1/2}}=50\,\,\text{days}\]


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