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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