Question

Silver; (atomic weight $=108gmo{l}^{-1})$ has a density of $10.5gc{m}^{-3}$. 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 $=108gmo{l}^{-1}$
Density $=10.5gc{m}^{-3}$
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 $x=7$