Given mass of gold(Au) is , m = 12.6 g
We know that molar mass of Au is 197 (g/mol)
So number of moles , n = mass/molar mass
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= 12.6 g / 197 (g/mol)
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= 0.064 mol
Therefore the number of atoms in the sample is 0.064 mol
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We know that 1 mole of any compound contains avagadro
number(6.023x1023) of atoms
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OR
197 g(1 mole) of Au contains 6.023x1023 atoms
12.6 g of Au contains N atoms
N = (6.023x1023 x12.6) / 197
  = 3.85x1022 atoms
Therefore the number of atoms in 12.6 g of pure gold is
3.85x1022 atoms