A) \[2\times {{10}^{-12}}m\]
B) \[2\times {{10}^{-10}}m\]
C) \[2\times {{10}^{-14}}m\]
D) \[2\times {{10}^{-7}}m\]
Correct Answer: B
Solution :
Volume of 1 kg of copper \[=\frac{1}{9\times {{10}^{3}}}{{m}^{3}}\] i.e., Volume of\[{{10}^{25}}\]atoms of copper \[=\frac{1}{9\times {{10}^{3}}}{{m}^{3}}\] Volume of 1 atom of copper \[=\frac{1}{9\times {{10}^{3}}\times {{10}^{25}}}{{m}^{3}}\] \[\Rightarrow \] \[\frac{4}{3}\pi {{r}^{3}}=\frac{1}{9\times {{10}^{28}}}\] \[\Rightarrow \] \[{{r}^{3}}=\frac{3}{4\pi \times 9\times {{10}^{28}}}\] \[\Rightarrow \] \[{{r}^{3}}=\frac{3}{4\times 3.14\times 3\times {{10}^{28}}}\] \[r=\sqrt[3]{\frac{1}{4\times 3.14\times 3\times {{10}^{28}}}}\] \[\Rightarrow \] \[r=\frac{1}{7.2\times {{10}^{9}}}\]
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