$2 \times 10^{8}$ atoms of carbon are arranged side by side. Calculate the radius of a carbon atom if the length of this arrangement is $2.4 \, cm$.

Length of the given arrangement $= 2.4 \, cm = 2.4 \times 10^{-2} \, m$.
Number of carbon atoms present $= 2 \times 10^{8}$.
Diameter of a carbon atom $= \frac{\text{Total length}}{\text{Number of atoms}} = \frac{2.4 \times 10^{-2} \, m}{2 \times 10^{8}} = 1.2 \times 10^{-10} \, m$.
Radius of a carbon atom $= \frac{\text{Diameter}}{2} = \frac{1.2 \times 10^{-10} \, m}{2} = 6.0 \times 10^{-11} \, m$.