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The Solid State

Question
CBSEENCH12005444

Write the formula of a compound which is made of two elements A and B. Atom A forms close-packed lattice while atom B occupies all tetrahedral voids.

Solution
For every atom in a close packed structure, there are two tetrahedral voids.

Let the number of close packed spheres be N, then:
The number of octahedral voids generated = N
The number of tetrahedral voids generated = 2N

Therefore formula of the compound is AB2