Question

In a cubic unit cell, $A$ atoms are present on alternate faces and $C$ atoms are present on alternate edges and body center of the cube. the simplest formula of a compound is:

• A. $AB{C}_4$
• B. $A_{2}B{C}_4$
• C. $A_3{C}_5$
• D. $AB{C}_2$

Answer 1

The correct option is C $A_3{C}_5$

Contribution of face centre A = $\frac{1}{2}$

Contribution of edge centre C = $\frac{1}{4}$

On body centre = 1

Total faces =6 Alternate faces occupied = half of 6

Effective number of $A=\frac{1}{2}\times \frac{1}{2}\times 6=\frac{3}{2}$ (Alternate faces)

Total edges = 12

Effective number of $C=\frac{1}{2}\times \frac{1}{4}\times 12+1$ (Alternate edges and body centre) $=\frac{5}{2}$

Formula = No of A : No of C

Formula $=A_{\frac{3}{2}}{C}_{\frac{5}{2}}=A_3{C}_5$

So correct option is C.