Question

Silver (atomic weight $ = 108g mol^{-1} $ ) has a density of
$ 10.5g 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

Answer 1

Ag crystallises in fee unit cell with 4 atoms per unit cell.
$ p = \frac{4 \times 108}{6.023 \times 10^{23} 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
$ = 1.25 \times 10^{7} \, \, \, \, \, \, [\because y \times 10^x]$
$ \Rightarrow \, \, x = 7 \Rightarrow y = 1.25 $