Question

A unit cell of calcium fluoride has four calcium ions. The number of fluoride ions in the unit cell is:
A.2
B.4
C.6
D.8

Answer 1

When we talk about a crystal lattice, we must know that it is a three dimensional arrangement of constituent particles (atoms, molecules, ions) which are of crystalline solids as points. The geometric arrangement of constituent particles of crystalline solids as point in space is called crystal lattice.

Complete step-by-step solution: In a crystal lattice we can see that each constituent particle can be represented by one point which is called a lattice point. These lattice points in the crystal lattice are joined by straight lines. By joining the lattice points with straight lines the geometry of the crystal lattice is formed.
Unit cell is the smallest portion of crystal lattice which when being repeated in different directions can produce an entire lattice. It can be characterized by six parameters which are three edges $\left( {a,{\text{ }}b{\text{ }}and{\text{ }}c} \right)$and angles between them $\left( {\alpha ,{\text{ }}\beta {\text{ }}and{\text{ }}\gamma } \right).$
We know that the formula for calcium fluoride is $Ca{F_2}$. The number of calcium ions which are present in this $= 4$. Thus, in order to maintain electrical neutrality, we have
$4 \times \left( { + 2} \right) + \left( x \right) \times \left( { - 1} \right) = 0$
Here, we must know that $\left( { + 2} \right)$ is charge on calcium on and $\left( { - 1} \right)$ is charge on fluoride ion
$\Rightarrow 8 - x = 0$
$\Rightarrow x = 8$
So, the number of ${F^ - }$ ions in the unit cell $= 8$.

Thus the answer is $\left( B \right)$

Note: When we talk about the dimensions on the edges, we must know that they are represented by $\left( {a,{\text{ }}b{\text{ }}and{\text{ }}c} \right)$. It is important to note that the edges of a unit cell may or may not be mutually perpendicular. The angle between $b{\text{ }}and{\text{ }}c$is represented by $\alpha$, between $a{\text{ }}and{\text{ }}c{\text{ }}by{\text{ }}\beta$ and between $a{\text{ }}and{\text{ }}b{\text{ }}by{\text{ }}\gamma$. There are two types of unit cells – Primitive and Centred Unit Cells.