2. Solved Papers
  3. AMU Medical

AMU Medical AMU Solved Paper-2013

  • question_answer
    Two radioactive materials \[{{X}_{1}}\] and \[{{X}_{2}}\] have decay constant \[6\lambda \] and \[3\lambda \] respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \[{{X}_{1}}\] to that of \[{{X}_{2}}\] will be \[\frac{1}{e}\] after a time

    A)  \[\frac{1}{6\lambda }\]                                

    B)  \[\frac{1}{3\lambda }\]

    C)  \[\frac{3}{6\lambda }\]                                

    D)  \[\frac{6}{9\lambda }\]

    Correct Answer: B

    Solution :

                     From                 \[{{N}_{1}}{{e}^{-{{\lambda }_{1}}\,t}}={{N}_{2}}{{e}^{-{{\lambda }_{2}}\,t}}\]                 \[\frac{{{N}_{1}}}{{{N}_{2}}}={{e}^{-({{\lambda }_{2}}-{{\lambda }_{1}})t}}\]                 \[\frac{1}{e}={{e}^{-({{\lambda }_{2}}-{{\lambda }_{1}})t}}\]       \[\left( Given\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{1}{e} \right)\]                 \[1=(6\lambda -3\lambda )\,t\]                 \[t=\frac{1}{3\lambda }\]


You need to login to perform this action.
You will be redirected in 3 sec spinner