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

  • question_answer
    The radius of germanium \[\left( Ge \right)\] nuclide is measured to be twice the radius of \[_{4}^{9}Be\]. The number of nucleons in \[Ge\] are

    A)  74

    B)  75    

    C)  72

    D)  73

    Correct Answer: C

    Solution :

    [c] We use the formula, \[R={{R}_{0}}{{A}^{1/3}}\] This represents relation between atomic mass and radius of the nucleus. For berillium,   \[{{R}_{1}}={{R}_{0}}{{(9)}^{1/3}}\] For germanium, \[{{R}_{2}}={{R}_{0}}{{A}^{1/3}}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{(9)}^{1/3}}}{{{(A)}^{1/3}}}\Rightarrow \frac{1}{2}=\frac{{{(9)}^{1/3}}}{{{(A)}^{1/3}}}\] \[\Rightarrow \,\,\,\,\,\frac{1}{8}=\frac{9}{A}\Rightarrow A=8\times 9=72.\]


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