2.00 x 10^22 atoms
The empirical formula for quartz is SiO2, so calculate the molar mass of quartz.
Silicon = 28.0855
Oxygen = 15.999
Molar mass = 28.0855 + 2 * 15.999 = 60.0835
Now divide the mass you have of quartz by its molar mass
1.00 g / 60.0835 g/mol = 0.016644 mol
Since you have 2 moles of oxygen atoms per mole of quartz, multiply by 2
0.016644 mol * 2 = 0.033288 mol
Finally, multiply by avogadro's number to get the number of atoms.
0.033288 mol * 6.0221409e+23 atoms/mol = 2.00465 x 10^22
Round to 3 significant figures to get 2.00 x 10^22