The well-known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are `4Ca^(2+)` ions and `8F^(-)` ions and that `Ca^(2+)` ions are arranged in a fce 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

The data provided suggests that the number of molecules per unit cell is 4.
`N_(A)=(zxxM)/(a^(3)xxd)`
Here `z=4, M=78.08 " g mol"^(-1), a=5.46xx10^(-8)cm, d=3.18gcm^(-3)`
Substituting the values in the above relation, we have
`N_(A)=(4xx78.08)/((5.46xx10^(-8))^(3)xx3.18)=(4xx78.08)/((5.46xx10^(-8))^(3)xx3.18)=(4xx78.08)/((5.46)^(3)xx10^(-24)xx3.18)=6.03xx10^(23)`