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In a cubic un...

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

A B C_{4}

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B

A_{2} B C_{4}

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C

A_{3} C_{5}

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D

A B C_{2}

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Solution

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.

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