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

Here, For fcc lattice,` Z =4, M =78.08g mol^(-1)`
` a=5.46xx10^(-8) cm`, " "`d=3.18g cm^(-3)`
`therefore` Using the formula, d=(Z.M)/(a^(3).N_(A))`
`therefore` " "`N_(a)=(Z.M)/(a^(3) .d)=(4xx78.08)/((5.46xx10^(-8))^(3)xx3.18)`
` N_(a)=6.033xx10^(23) mol^(-1))`