JEE Main · 2011 · 10 Apr 2011 · Offline · Solid State

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In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is :

(A) $AB_{2}$
(B) $A_{2} B_{3}$
(C) $A_{2} B_{5}$ ✓ Correct
(D) $A_{2} B$

Answer: (C)

Solution

In the face-centred cubic cell the corner atoms

A

contribute

8 \times \frac{1}{8} = 1

atom, and the face-centre atoms

B

would contribute

6 \times \frac{1}{2} = 3

. With one face-centre

B

missing, that count falls to

\frac{1}{2} \times 5 = 2.5

. The ratio

A : B = 1 : 2.5

clears to whole numbers as

2 : 5

, so the formula is

A_{2} B_{5}

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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