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.
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?
2 Answers
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 =8x1/8=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 of both P and Q is 8.
The atom at the corner makes \(\frac{1}{8}\) contribution while atom at body centre makes 1 contribution to the unit cell.
No. of atoms of Q per unit cell = 8 × \(\frac{1}{8}\) = 1
No. of atoms of P per unit cell = 1 × 1 = 1
Therefore, formula of the compound is PQ.
The atom at the body centre would be in contact with all the atoms at the corners. Hence, the coordination number of P is 8.
Similarly, the coordination number of Q is 8 because it is shared by 8 other atoms.