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Question

# In a face centered 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 centered points, the formula of the compound is:

A
A2B5
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B
A2B3
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C
AB2
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D
A2B
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Solution

## The correct option is A A2B5In a face centered cubic lattice, atom (A) occupies the corner positions. There are 8 corner positions and each position contributes one eighth to the unit cell. Hence, total number of (A) atoms per unit cell. =18×8=1 Atom (B) occupies face centre positions. There are six face centre positions in one unit cell. One atom of (B) is missing from one of the face centered points. Thus, there are 5 face centre positions that are occupied with (B). Each such positions contributes one half to the unit cell. Hence, total number of (B) atoms per unit cell =12×5=2.5 The formula of the compound is AB2.5 or A2B5

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