the atomic weight is numerically equivalent to the molar mass.
therefore molar mass of gold is - 197.2 g/mol
avagadros number states that 1 mol of any substance is made of 6.022 x 10²³ units. These units could be atoms making up elements or molecules making up compounds.
1 mol of gold is made of 6.022 x 10²³ atoms of gold
since 1 mol weighs 197.2 g
therefore if 197.2 g of gold contains - 6.022 x 10²³ atoms of gold
then 7.5 g contains - 6.022 x 10²³ x 7.5/ 197.2 = 2.29 x 10²² atoms of gold
answer is 2.29 x 10²² atoms of gold