$10 g$ of Calcium carbonate contains

 Using the formula: $\mathrm{moles}=\frac{\mathrm{given} \mathrm{mass}}{\mathrm{molecular} \mathrm{mass}}$

Molecular weight of calcium carbonate is 100 (Ca=40, C=12, O=16)

Moles of calcium carbonate will be = $\frac{10}{100}=0.1mole$= 0.1 g atom.

Since 1mole = $6.022\times {10}^{23}$ atoms

Therefore 0.1mole= $6.022\times {10}^{22}$atoms of calcium

Hence the correct option is (C).