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\(2 \times 10^8\) atoms of carbon are arranged side by side. Calculate the radius of carbon atom if the length of this arrangement is \(2.4 \mathrm{~cm}\).
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Total length \(=2.4 \mathrm{~cm}\).
Total number of atoms along the length \(=2 \times 10^8\) atoms
\(\therefore\) Diameter of each atom \(=\frac{2.4 \mathrm{~cm}}{2 \times 10^8}=1.2 \times 10^{-8}\)
\(\therefore\) Radius of the atom \(=\frac{1.2 \times 10^{-8} \mathrm{~cm}}{2}\) \(\quad=0.6 \times 10^{-8} \mathrm{~cm}=0.6 \times 10^{-9} \mathrm{~m}=0.6 \mathrm{~nm}\).
Total number of atoms along the length \(=2 \times 10^8\) atoms
\(\therefore\) Diameter of each atom \(=\frac{2.4 \mathrm{~cm}}{2 \times 10^8}=1.2 \times 10^{-8}\)
\(\therefore\) Radius of the atom \(=\frac{1.2 \times 10^{-8} \mathrm{~cm}}{2}\) \(\quad=0.6 \times 10^{-8} \mathrm{~cm}=0.6 \times 10^{-9} \mathrm{~m}=0.6 \mathrm{~nm}\).
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