Question

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 $10^{-12} \,m^2$ can be expressed in scientific notation as $y \times 10^x$. The value of $x$ is

• A. 6
• B. 3
• C. 5
• D. 7

Answer 1

Answer: (D)

Given, atomic weight $= 108 \,g \,mol^{-1}$
Density $= 10.5 \,g \,cm^{-3}$
Surface area $= 10^{-12} m^2$
Volume of one silver atom $= 4/3\pi r^3$
$\because$ Density $ = \frac{\text{Mass}}{\text{Volume}}$
$\Rightarrow $ Volume $= \frac{\text{Mass}}{\text{Density}}$
or $\frac{4}{3} \pi r^3 = \frac{108}{6.023 \times 10^{23} \times 10.5}$
$r^3 = \frac{108 \times 3}{6.023 \times 10^{23} \times 10.5 \times 4 \times 3.14}$
$r^3 = 0.40 \times 10^{-23} = 4\times 10^{-24}$
or $ r = 1.58 \times 10^{-8} \,cm$
No. of silver atoms $(n)$ on a surface area of $10^{-12} m^2$
can be given by $10^{-12} = \pi r^2 \times n$
$ n = \frac{10^{-12}}{3.14 \times ( 1.58 \times 10^{-10})^2} = 0.127 \times 10^8$
$\Rightarrow n = 1.27 \times 10^7 $
$y \times 10^x $ or $ x = 7$