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Question

# A binary solid has a primitive cubical structure with B− ions constituting the lattice points and A+ ions occupying 25% of its tetrahedral holes. The molecular formula of the crystal is:

A
A2B
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B
AB3
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C
AB2
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D
A2B3
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E
A2B5
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Solution

## The correct option is C AB2Let number of octahedral holes in the lattice =x∴ Number of tetrahedral holes in the lattice =2x(∵ Number of tetrahedral holes =2× number of octahedral holes) Now, A+ ions occupy 25% of tetrahedral holes. Hence, number of tetrahedral holes' occupied in the lattice =2x×25% =2x×25100=x2Since, number of octahedral holes = Number of lattice points. ∴ Number of octahedral holes =x ∴ Molecular formula of the crystal is Ax/2Bx or AB2

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