Chemistry - Mole Concept Question with Solution | TestHub

Volume of one mole of silver atoms $=\frac{108}{10.5}{\mathrm{cm}}^3/$ mole Volume of one silver atom $=\frac{108}{10.5}\times \frac{1}{6.022\times 10^{23}}{\mathrm{cm}}^3$ So, $$\begin{array}{rl}\frac{4}{3}\pi R^3& =\frac{108}{10.5}\times \frac{1}{6.022\times 10^{23}}=1.708\times 10^{-23}\\ R^3& =0.407\times 10^{-23}{\mathrm{cm}}^3\\ & =0.407\times 10^{-29}{\mathrm{m}}^3\end{array}$$ Area of each silver atom $$\pi R^2=\pi \times {\left(0.407\times 10^{-29}{\mathrm{m}}^3\right)}^{2/3}$$ So number of silver atoms in given area $$=\frac{10^{-12}}{{\left(0.407\times 10^{-29}{\mathrm{m}}^3\right)}^{2/3}}=\frac{10^8}{(\pi \times 2)}=1.6\times 10^7=y\times 10^x\text{ so, }x=7$$