Question

Silver $(\text{atomic weight}=108{\text{gmol}}^{-1})$ has a density of $10.5{\text{gcm}}^{-3}$. 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:

Answer 1

Step1:

$1c{m}^3$ of silver weights 10.5 g.
The number of moles of this would be: $10.5/108mol$
$1cm$ would have $(\frac{10.5}{108}{)}^{1/3}$ moles,
$1c{m}^2$ would have $(\frac{10.5}{108}{)}^{2/3}$ moles

Step 2:
$\therefore {10}^{-12}{m}^3\left({10}^{-8}c{m}^2\right)$ would have
$(\frac{10.5}{108}{)}^{2/3}\times {10}^{-8}=1.5\times {10}^7$ atoms.

Hence, the value of x is $1.5\times {10}^5$ atoms.