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

To calculate Avogadro's number using the provided information about calcium fluoride (CaF₂), we will follow these steps:

### Step 1: Understand the Unit Cell Structure
In the face-centered cubic (FCC) lattice of calcium fluoride:
- There are 4 \( \text{Ca}^{2+} \) ions per unit cell.
- There are 8 \( \text{F}^{-} \) ions per unit cell.
- The total number of ions in one unit cell is \( 4 + 8 = 12 \).

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