Question

The crystalline solids have definite orderly arrangement of their constituent particles in three dimensions known as lattice. The smallest repeating part in the lattice is known as unit cell. The unit cell are described as simple cubic face centred and body centred unit cell.
For the stable ionic crystalline structures, there is definite radius ratio limit for a cation to fit perfectly in the lattice of anions called radius ratio rule. This also defines the coordination number of an ion.
(ii) In a cubic lattice ABC, A atom present at all corners except one at corner which is occupied by B atoms. C atoms are present at face centres. The formula of the compound is:

• A. $A_7{B}_{24}C$
• B. $AB{C}_3$
• C. $A_{8}B{C}_7$
• D. $A_{7}B{C}_{24}$

Answer 1

The correct option is D $A_{7}B{C}_{24}$

Number of atom of A $=7\times \frac{1}{8}=\frac{7}{8}$

Number of atom of B $=1\times \frac{1}{8}=\frac{1}{8}$

Number of atom of C $=6\times \frac{1}{2}=3$

Formula of the compound is $A_{\frac{7}{8}}{B}_{\frac{1}{8}}{C}_3$ or $A_{7}B{C}_{24}$