NEET AIPMT SOLVED PAPER MAINS 2012

  • 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 t1 when \[\frac{1}{3}\] of it had decayed is                                              

    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 \[{{t}_{1}},\] \[\frac{1}{{{2}^{{{t}_{1}}/{{T}_{1/2}}}}}=\frac{2}{3}\] \[\frac{{{2}^{{{t}_{2}}/{{T}_{1/2}}}}}{{{2}^{{{t}_{1}}/{{T}_{1/2}}}}}=2\] \[{{\frac{^{{{t}_{2}}-{{t}_{1}}}}{{{_{2}}^{{{T}_{1/2}}}}}}_{=2}}\] \[{{t}_{2}}-{{t}_{1}}={{T}_{1/2}}=50\,days\]


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