JEE Advance - Chemistry (2010 - Paper 2 Offline - No. 2)
Silver (atomic weight = 108 g mol-1) has a density of 10.5 g.cm-3. The number of silver atoms on a surface of area 10-12 m2 can be expressed in scientific notation as y $$\times$$ 10x. The value of x is?
Answer
7
Explanation
Given, atomic weight $=108 \mathrm{~g} \mathrm{~mol}^{-1}$
Density $=10.5 \mathrm{~g} \mathrm{~cm}^{-3}$
Surface area $=10^{-12} \mathrm{~m}^2$
Volume of one silver atom $=4 / 3 \pi r^3$
$$ \because \text { Density }=\frac{\text { Mass }}{\text { Volume }} \Rightarrow \text { Volume }=\frac{\text { Mass }}{\text { Density }} $$
$\begin{aligned} & \text { or } \frac{4}{3} \pi r^3=\frac{108}{6.023 \times 10^{23} \times 10.5} \\\\ & r^3=\frac{108 \times 3}{6.023 \times 10^{23} \times 10.5 \times 4 \times 3.14} \\\\ & r^3=0.40 \times 10^{-23}=4 \times 10^{-24} \\\\ & \text { or } r=1.58 \times 10^{-8} \mathrm{~cm} \end{aligned}$
No. of silver atoms on a surface area of $10^{-12} \mathrm{~m}^2$ can be given by $10^{-12}=\mathrm{p} r^2 \times n$
$\begin{aligned} & n=\frac{10^{-12}}{3.14 \times\left(1.58 \times 10^{-10}\right)^2}=0.127 \times 10^8 \\\\ \Rightarrow & n=1.27 \times 10^7 \text { or } x=7\end{aligned}$
Density $=10.5 \mathrm{~g} \mathrm{~cm}^{-3}$
Surface area $=10^{-12} \mathrm{~m}^2$
Volume of one silver atom $=4 / 3 \pi r^3$
$$ \because \text { Density }=\frac{\text { Mass }}{\text { Volume }} \Rightarrow \text { Volume }=\frac{\text { Mass }}{\text { Density }} $$
$\begin{aligned} & \text { or } \frac{4}{3} \pi r^3=\frac{108}{6.023 \times 10^{23} \times 10.5} \\\\ & r^3=\frac{108 \times 3}{6.023 \times 10^{23} \times 10.5 \times 4 \times 3.14} \\\\ & r^3=0.40 \times 10^{-23}=4 \times 10^{-24} \\\\ & \text { or } r=1.58 \times 10^{-8} \mathrm{~cm} \end{aligned}$
No. of silver atoms on a surface area of $10^{-12} \mathrm{~m}^2$ can be given by $10^{-12}=\mathrm{p} r^2 \times n$
$\begin{aligned} & n=\frac{10^{-12}}{3.14 \times\left(1.58 \times 10^{-10}\right)^2}=0.127 \times 10^8 \\\\ \Rightarrow & n=1.27 \times 10^7 \text { or } x=7\end{aligned}$
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