Question

A cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

A cubic solid is made up of two elements P and Q. Atoms Q are present at the corners of the cube and atom P at the body centre. What is the formula of the compound?

Answer 1

It is given that the atoms of Q are present at the corners of the cube.

Therefore, number of atoms of Q in one unit cell = `8 xx 1/8`

= 1

It is also given that the atoms of P are present at the body centre.

Therefore, number of atoms of P in one unit cell = 1

This means that the ratio of the number of P atoms to the number of Q atoms, P : Q = 1 : 1

Hence, the formula of the compound is PQ.

The coordination number refers to the number of nearest neighbouring atoms surrounding a given atom. For P, since it is surrounded by Q atoms, we have:

Coordination number of P = 8

For Q, which is surrounded by P atoms, the coordination number is also:

Coordination number of Q = 8

Thus, the formula of the compound is PQ, and the coordination numbers of both P and Q are 8.

Since the lattice is body-centred cubic, the coordination number of each atom is 8.