A gold sample contains 90% of gold and the rest copper.

Mass of pure gold in one gram of the sample $=\frac{1 \times 90}{100}=0.9 \mathrm{~g}$

No. of moles of gold present $=\frac{\text { Mass of gold }}{\text { Molar atomic mass }}=\frac{(0.9 \mathrm{~g})}{\left(0197 \mathrm{~g} \mathrm{~mol}^{-1}\right)}=0.0046 \mathrm{~mol}$

One mole of gold contains atoms $=\mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23}$

$0.0046$ mole of gold contains atoms $=6.022 \times 10^{23} \times 0.0046=2.77 \times 10^{21}$