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 `8F^(-)` ions and that `Ca^(2+)` ions are arranged in a fcc-lattice. The `F^(-)` 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 xx 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)`)

Explanation

`d = (Z xx M)/(a^(3) xx N_(A))`
For fcc lattice Z = 4
3.18 g `cm^(-3) = (4 xx 78.08 g mol^(-1))/((5.46 xx 10^(-8)cm)^(3) xx N_(A))`
`N_(A) = (4 xx 78.08 g mol^(-1))/((5.46 xx 10^(-8)cm)^(3) xx 3.18 g cm^(-3))`
`N_(A) = 6.033 xx 10^(23) mol^(-1)`