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JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Critical Thinking

  • question_answer
    The ratio of radii of nuclei \[_{13}A{{l}^{27}}\] and \[_{52}{{X}^{A}}\] is 3 : 5. The number of neutrons in the nuclei of X will be

    A)            52  

    B)            73

    C)            125                                           

    D)            13

    Correct Answer: B

    Solution :

                \[r\propto {{A}^{1/3}}\] Þ \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)}^{1/3}}\]                    Þ \[\frac{3}{5}={{\left( \frac{27}{A} \right)}^{1/3}}\]Þ \[\frac{27}{125}=\frac{27}{A}\]Þ \[A=125\]                    Number of nuclei in atom X \[=A-52=125-52=73.\]


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