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The well known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are 4 Ca$^{2+}$ ions and 8 $F^−$ ions and that $Ca^{2+}$ ions are arranged in a fcc lattice. The fluoride ions fill all the tetrahedral holes in the face centred cubic lattice of $Ca^{2+}$ ions. The edge of the unit cell is $5.46 × 10^{−8}$ cm in length. The density of the solid is $3.18 g cm^{−3}$. Use this information to calculate Avogadro's number. (Molar mass of $CaF_2 = 78.08 g mol^{−1}$)

$6.03\times 10^{23}$