Question

A face-centred cubic Lattice Is made up of two types of atoms, atom A and atom B in which A occupies the corner positions and B occupies the face centres. If atoms from one corner is absent per unit cell, the empirical formula of the remaining solid would be:

• A. $A_7{B}_3$
• B. $A_7{B}_9$
• C. $A_7{B}_{10}$
• D. $A_7{B}_{24}$

Answer 1

The correct option is D $A_7{B}_{24}$

Number of atoms of A from corners of unit cell $=\frac{7}{8}$

Number of atoms of B from face of unit cell $=3$

Thus

$A:B=\frac{7}{8}:3$

Or $=7:24$

Therefore the formula is $A_7{B}_{24}$