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)
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Answer:
Correct Answer: 37. $(7)$
Solution:
- Ag crystallises in fcc unit cell with $4$ atoms per unit cell.
$\rho=\dfrac{4 \times 108}{6.023 \times 10^{23} \times a^{3}}=10.5$ $ 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
$ =\dfrac{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
$ =1.25 \times 10^7 .\quad$ $ {\left[\because \quad y \times 10^x\right]}$
$ \Rightarrow \quad x=7 \Rightarrow y=1.25$
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