Step 1. Calculate the mass of pure gold
If the mass of the ring is 300 mg, then
#"Mass of Au" = "300 mg" × (20 color(red)(cancel(color(black)("kt"))))/(24 color(red)(cancel(color(black)("kt")))) = "250 mg"#
Step 2. Calculate the moles of #"Au"#
#"Moles of Au" = 0.250 color(red)(cancel(color(black)("g Au"))) × "1 mol Au"/(179 color(red)(cancel(color(black)("g Au")))) = "0.001 269 mol Au"#
Step 3. Calculate the atoms of #"Au"#
#"Atoms of Au" = "0.001 269" color(red)(cancel(color(black)("mol Au"))) × (6.022 × 10^23color(white)(l) "atoms Au")/(1 color(red)(cancel(color(black)("mol Au"))))#
#= 7.64 × 10^20 color(white)(l)"atoms Au"#
