Question

A compound formed by elements X and Y crystallizes in a cubic structure in which the X atoms are at the corners of a cube and the Y atoms are at the face-centres. The formula of the compound is:
(A) ${X_3}Y$
(B) XY
(C) $X{Y_2}$
(D) $X{Y_3}$

Answer 1

We are given a compound which is formed by X and Y elements. This element crystallizes in a cubic lattice. The positions of the atoms of elements X and Y are specified in the cubic lattice. Hence, using these positions we will calculate the total number of atoms of each element X and Y present in a cubic lattice and then it will help us to deduce the formula of this compound.

Complete answer:
A compound formed by elements X and Y crystallizes in a cubic structure. We are given that the X element is present at all the corners of the cube and the Y atoms are at the face-centres. Therefore, we can conclude that it is a F.C.C crystal lattice (Face-centred cubic).
The X atoms present at the corners of unit cell is shared by 8 unit cells. Therefore, one-eighth of a X atom belongs to an individual unit cell.
$X = \dfrac{1}{8} \times 8$
$X = 1$
Therefore, there is one atom of X present in a cube.
Y atoms which are present on the face centres are shared by two individual unit cells and hence, one-half of an X atom belongs to an individual unit cell.
$Y = \dfrac{1}{2} \times 6$
$Y = 3$
So, there are three atoms of Y in a cube.
Hence, the formula of given compound is found to be $X{Y_3}.$

Therefore, the correct option is (D) $X{Y_3}.$

Note:
Some of the other common crystal structures are simple cubic cells (s.c.c), Hexagonal, Body-centred cubic (B.c.c.) and face-centred cubic (f.c.c.). Some examples of face-centred cubic lattice are potassium chloride (KCl), sodium chloride (NaCl) and Sodium fluoride (NaF). Different crystal lattices have different characteristic properties.