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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Self Evaluation Test - Nuclei

  • question_answer
    A radioactive material of half-life ln2 was produced in a nuclear reactor. Consider two different instants A and B. The number of undecayed nuclei at instant B was twice of that of instant A. If the activities at instants A and B are  \[{{A}_{1}}\] and \[{{A}_{2}}\] respectively then the difference in the age of the sample at these instants equals.

    A)  \[\left| \ell n\left( \frac{2{{A}_{1}}}{{{A}_{2}}} \right) \right|\]

    B)  \[\ell n2\left| \ell n\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right) \right|\]

    C)  \[\left| \ell n\left( \frac{{{A}_{1}}}{2{{A}_{2}}} \right) \right|\]

    D)  \[\ell n2\left| \ell n\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right) \right|\]

    Correct Answer: C

    Solution :

    [c] \[{{A}_{1}}=(\lambda {{N}_{0}}){{e}^{-\lambda {{t}_{1}}}}\]             .....(i) \[{{A}_{2}}=(\lambda 2{{N}_{0}}){{e}^{-\lambda {{t}_{2}}}}\]                ....(ii) \[{{t}_{1}}-{{t}_{2}}=\frac{1}{\lambda }\ell n\left( \frac{{{A}_{2}}}{2{{A}_{1}}} \right)=\ell n\left( \frac{{{A}_{2}}}{2{{A}_{1}}} \right)\]


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