Question

Silver ($108$ g/mol) 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. $7$
• B. $3$
• C. $5$
• D. $8$

Answer 1

Answer: (A)

$7$

Ag crystallizes in a fcc structure.
The volume of $1$ unit cell $=a^3=\frac{M\times z}{N_0\times d}=\frac{108\times 4}{6.023\times {10}^{23}\times 10.5}=6.83\times {10}^{-23}$ cm${}^3$ $=6.83\times {10}^{-29}$ m${}^3$
Hence, the edge length, $a=4.09\times {10}^{-10}$ m
$a^2=1.678\times {10}^{-19}$
The number of silver atoms on the surface area of ${10}^{-12}$ m${}^2$ is approximately $\frac{{10}^{-12}}{1.678\times {10}^{-19}}=y\times {10}^7=y\times {10}^x$
Hence, the value of $x$ is $7$.