JEE Main · 2005 · 08 May 2005 · Offline · Solid State

An ionic compound has a unit cell consisting of

A

ions at the corners of a cube and

B

ions on the centres of the faces of the cube. The empirical formula for this compound would be

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

Answer: (C)

Solution

Count how much of each ion a single cube actually owns. The A ions sit at the eight corners, and since a corner is shared between eight neighbouring cubes, each contributes only

\frac{1}{8}

, giving

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

A ion per cell. The B ions sit on the six faces, and a face is shared between two cubes, so each contributes

\frac{1}{2}

, giving

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

B ions. The ratio

1 : 3

fixes the empirical formula as

AB X_{3}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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