First let us calculate the mass of diamond (pure Carbon).
mass = 2.8 carat * (0.20 grams / carat)
mass = 0.56 grams
The molar mass of Carbon is 12 g / mol and the Avogadros number is 6.022 x 10^23 atoms / mol, therefore:
Carbon atoms = 0.56 grams * (1 mol / 12 g) * (6.022 x 10^23 atoms / mol)
Carbon atoms = 2.81 x 10^22 atoms