The density of $C a F_{2}$ (fluorite structure) is 3.18 $g / c m^{3}$ . The length of the side of the unit cell is:

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Solution

Density of $C a F_{2} = 3.18$

Molar Mass of $C a F_{2} = 78 g / m o l .$

Using the Formula,
$D e n s i t y = \frac{M a s s}{V o l u m e}$ .

$V o l u m e = \frac{M a s s}{D e n s i t y}$

$V o l u m e = \frac{78}{3.18}$

$V o l u m e = 24.53$ cubic units.

Now, Volume of one cube of $C a F_{2} = (S i d e)^{3}$

$S i d e = \sqrt[3]{V o l u m e}$

$S i d e = \sqrt[3]{24.53}$

$S i d e = 2.905 u n i t s .$

Hence, the Length of the side of the unit cell of the $C a F_{2} i s 2.905 u n i t s$ .

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