Question

Silver (atomic weight $=108$ g mol${}^{-1}$) has a density of $10.5$ $gc{m}^{-3}$. 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. 7
• B. 8
• C. 6
• D. 9

Answer 1

The correct option is A 7

$D=\frac{M}{V}\Rightarrow 10.5g/cc$ means in $1$ cc $10.5$ g of $Ag$ is present.
Number of atoms of $Ag$ in $1cc=\frac{10.5}{108}\times N_A$
In $1$ cm, number of atoms of $Ag$ $=\sqrt[3]{3\frac{10.5}{108}{N}_A}$

In $1c{m}^2$, number of atoms of $Ag=(\frac{10.5}{108}{N}_A{)}^{2/3}$

In ${10}^{-12}{m}^2$ or ${10}^{-8}c{m}^2$, number of atoms of $Ag=(\frac{10.5}{108}{N}_A{)}^{2/3}\times {10}^{-8}=(\frac{1.05\times 6.022\times {10}^{24}}{108}{)}^{2/3}\times {10}^{-8}$

$=1.5\times {10}^{7}atoms$

Hence, $x=7$.