Question

Atoms C and D form FCC crystalline structure. Atom C is present at the corners of the cube and D is at the faces of the cube. What is the formula of the compound?

Answer 1

Hint: In the above given question we need to calculate the formula of the compound of C and D when they are arranged in FCC. The effective number of atoms of D is three and of C is just one and therefore they would have them as their lower coefficient in the molecular formula.

Complete answer:
In the above given question, we are asked to calculate the formula of C and D when both the toms are arranged in the face centred cubic structure.
Now what is a face centred cubic structure? In an FCC what happens is that anion is arranged at the edges of the cube of one atom of the unit of the compound and the cation is placed at all the faces of the cubic structure. Now the atoms when arranged at the edges and the faces also share the atoms with the adjacent units, due to which the effective number of atoms of cations and anions need to be calculated.
Now there are C arranged at the edges of the cube. Now the cube has eight edges and at each edge there are eight other units therefore the effective number of C in a unit is $8 \times \dfrac{1}{8} = 1$, just equal to one.
Now the atoms of D are arranged at the faces of the cube unit and also each face gets shared by one other face so the effective number of atoms of D is equal to $6 \times \dfrac{1}{2} = 3$, is just three.
Now using the information given above we can say that there are three units of D and one unit of C in a unit of the compound of C and D when arranged in the FCC way.
Therefore, the formula would look like $C{D_3}$.
The formula of the compound when C and D are arranged in FCC is $C{D_3}$.

Note:
There are many atoms which form their compound in the face centred cubic way. Some of the examples of such metals are aluminium, copper, nickel, gamma iron, gold and silver. One of the well-known compounds arranged in FCC is sodium chloride or table salt.