AIIMS AIIMS Solved Paper-2003

  • question_answer
    A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance expressed in days is:

    A)  2.5                        

    B)        5                            

    C)        10                         

    D)        20

    Correct Answer: C

    Solution :

    From Rutherford and Soddy law for radioactive decay \[{{i}_{2}},\] where \[{{h}^{1/2}}\] and N are number of atom in a radioactive substance at time t = 0 and t =t and \[h\] is decay constant. Also, half-life \[{{h}^{3/2}}\] \[{{h}^{2}}\]   \[\frac{N}{{{N}_{0}}}\,={{e}^{\frac{0.693}{{{T}^{1/2}}}t}}\] Given, \[[{{M}^{-1}}L{{T}^{-2}}A]\]days, \[[{{M}^{-2}}L{{T}^{-2}}{{A}^{-1}}]\] \[[ML{{T}^{-2}}{{A}^{-2}}]\]  \[[ML{{T}^{-1}}{{A}^{-1}}]\] \[{{\beta }^{-}}\]  \[+\frac{G{{M}_{e}}m}{R}=\frac{1}{2}mv_{e}^{2}\] \[{{M}_{e}}\] \[\therefore \] days.


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