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

  • question_answer
    The ratio of half-life times of two elements A and B is  \[\frac{{{T}_{A}}}{{{T}_{B}}}\]. The ratio of respective decay constant \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}},\] is

    A)  \[{{T}_{B}}/{{T}_{A}}\]

    B)  \[{{T}_{A}}/{{T}_{B}}\]

    C)  \[\frac{{{T}_{A}}+{{T}_{B}}}{{{T}_{A}}}\]

    D)  \[\frac{{{T}_{A}}-{{T}_{B}}}{{{T}_{A}}}\]

    Correct Answer: A

    Solution :

    [a]  \[{{T}_{1/2}}=\frac{In2}{\lambda }\,\,\therefore \,\,\lambda =\frac{In2}{{{T}_{1/2}}}\] \[\Rightarrow \,\,\,\,\,\,{{\lambda }_{A}}=\frac{In2}{{{T}_{A}}},\,\,\,\,{{\lambda }_{B}}=\frac{In2}{{{T}_{B}}}\Rightarrow \frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{{{T}_{B}}}{{{T}_{A}}}.\]


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