Answer
$n = 5.90 \times 10^{28} m^{-3}$
Work Step by Step
$n = \frac{d}{M}$
where
d = Mass density
M = Mass of single gold atom
n = Number of conduction electrons per unit volume
molar mass of gold $ A = 197 g/mol$
Find the M first
$ M = \frac{A}{N_A}$
where $N_A$ is $6.022 \times 10^{23}/mol$
$ M = \frac{197 g/mol}{6.022 \times 10^{23}/mol}$
$M = 3.27\times 10^{-22} g$
So,
$n = \frac{d}{M}$
$n = \frac{(19.3 g/cm^3)(10^6 cm^3/m^3)}{3.27\times 10^{-22} g} $
$n = 5.90 \times 10^{28} m^{-3}$
