The well know mineral flourite is chemically calcium fluoride. It is a well known fact that in one unit cell of this mineral, there are four `Ca^(2+)` ions and eight `F^(-)` ions and `Ca^(2+)` ions are arranged in f.c.c. lattice. The `F^(-)` ions fill all the tetrahedral holes in the face centred cubic lattice of `Ca^(2+)` ions. The edge length of the unit cell is `5.46xx10^(-8)` cm. The density of the solid is `3.18"g cm"^(-3)`. Use this information to calculate Avogadro's number (Molar mass of `CaF_(2)=78.0"g mol"^(-1)`)

Explanation

We know that `rho=(ZxxM)/(a^(3)xxN_(0)xx10^(-30))orN_(0)=(ZxxM)/(a^(3)xxrhoxx10^(-30))`
Edge length of unit cell (a) = `5.46xx10^(-8)` cm= 564 pm = 564
No. of atoms per unit cell (Z) = 4
Density of unit cell `(rho)=3.18"g cm"^(-3)`
Molar mass of `CaF_(2)(M)=78.0"g mol"(-1)`
Avogadro's Number (No.) = `=(4xx(78.0"g mol"^(-1)))/((546)^(3)(3.18"gcm"^(-3))xx(10^(-30)"cm"^(3)))`
`=(4xx(78.0"g mol"^(-1)))/(1.63xx10^(8)(3.18"g cm"^(-3))xx(10^(-30)"cm"^(3)))=6.02xx10^(23)"mol"^(-1)`