JEE Main & Advanced Chemistry Structure of Atom Question Bank Critical Thinking

  • question_answer The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number \[A\] is given by \[1.25\times {{10}^{-13}}\times {{A}^{1/3}}cm\] Radius of atom is one \[{AA}\]. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is [NCERT 1983]

    A) \[1.0\times {{10}^{-3}}\]              

    B) \[5.0\times {{10}^{-5}}\]

    C) \[2.5\times {{10}^{-2}}\]              

    D) \[1.25\times {{10}^{-13}}\]

    Correct Answer: D

    Solution :

    Radius of nucleus \[=1.25\,\times {{10}^{-13}}\times {{A}^{1/3}}\,cm\]                   \[=1.25\,\times {{10}^{-13}}\times {{64}^{1/3}}\]\[=5\times {{10}^{-13}}\,cm\]                    Radius of atom = \[1\text{{ }\!\!\mathrm{AA}\!\!\text{ }}\,={{10}^{-8}}cm.\]                    \[\frac{\text{Volume of nucleus}}{\text{Volume of atom}}\]\[=\frac{(4/3)\pi \,{{(5\times {{10}^{-13}})}^{3}}}{(4/3)\pi \,{{({{10}^{-8}})}^{3}}}\]                                 \[=1.25\,\times {{10}^{-13}}\].

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