Solid State - Result Question 37
####37. 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
(2010)
Show Answer
Answer:
Correct Answer: 37. (7)
Solution:
- Ag crystallises in fcc unit cell with 4 atoms per unit cell.
$\rho=\frac{4 \times 108}{6.023 \times 10^{23} \times a^{3}}=10.5 g cm^{-3}$.
$\Rightarrow a^{3}($ Volume of unit cell $)=6.83 \times 10^{-23} cm^{3}$
$\Rightarrow a=4 \times 10^{-8} cm=4 \times 10^{-10} m$
$\Rightarrow$ Surface area of unit cell $=a^{2}=1.6 \times 10^{-19} m^{2}$
$\Rightarrow$ Number of unit cells on $10^{-12} m^{2}$ surface
$$ =\frac{10^{-12}}{1.6 \times 10^{-19}}=6.25 \times 10^{6} $$
$\because$ There are two atoms (effectively) on one face of unit cell Number of atoms on $10^{-12} m^{2}$ surface $=2 \times$ number of unit cell
$$ \begin{aligned} & =1.25 \times 10^{7} . \\ & \Rightarrow x = 7 \end{aligned} \quad\left[\because y \Rightarrow y \times 10^{x}\right] $$
