JEE Main & Advanced Chemistry Nuclear chemistry Question Bank Critical Thinking Nuclear chemistry

  • question_answer A radioactive nucleide X decays at the rate of \[1.00\times {{10}^{5}}\] disintegration \[{{s}^{-1}}{{g}^{-1}}\]. Radium decays at the rate of \[3.70\times {{10}^{10}}\] disintegration \[{{s}^{-1}}{{g}^{-1}}\]. The activity of X  in millicuries \[{{g}^{-1}}\] \[(m\,ci\,{{g}^{-1}})\] is               [MP PET 2001]

    A)            0.027                                       

    B)            \[0.270\times {{10}^{-5}}\]

    C)            0.00270                                   

    D)            0.000270

    Correct Answer: B

    Solution :

           \[\frac{d{{x}_{1}}}{dt}=\lambda {{N}_{1}},\,\,1\times {{10}^{5}}=\lambda {{N}_{1}}\]                    \[\frac{d{{x}_{2}}}{dt}=\lambda {{N}_{2}},\,3.7\times {{10}^{10}}=\lambda {{N}_{2}}\]                    \[\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{1\times {{10}^{5}}}{3.7\times {{10}^{10}}}=\frac{1\times {{10}^{-5}}}{3.7}=0.27\times {{10}^{-5}}\].

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