DUMET Medical DUMET Medical Solved Paper-2008

  • question_answer
    Activity of radioactive element decreased to one-third of original activity \[{{R}_{o}}\] in 9 yr. After further 9 yr, its activity will be

    A)  \[{{R}_{o}}\]

    B)  \[\frac{2}{3}{{R}_{o}}\]

    C)  \[\frac{{{R}_{o}}}{9}\]

    D)  \[\frac{{{R}_{o}}}{6}\]

    Correct Answer: C

    Solution :

     Activity \[R+{{R}_{0}}{{e}^{-\lambda t}}\] \[\frac{{{R}_{0}}}{3}={{R}_{0}}{{e}^{-9\lambda }}\,\,\,\Rightarrow \,\,\,{{e}^{-9\lambda }}=\frac{1}{3}\] ?. (i) After further \[9\,yr\,R={{\operatorname{Re}}^{-\lambda t}}=\frac{{{R}_{0}}}{3}{{e}^{-9\lambda }}\] ... (ii) From Eqs. (i) and (ii), \[R=\frac{{{R}_{0}}}{9}\]


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