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Question

A mineral having formula $$AB_{2}$$ crystallises in the cubic close-packed lattice, with the $$A$$ atoms occupying the lattice points. Hence coordination number of $$A$$ and $$B$$ atoms are:


A
4,8
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B
4,4
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C
8,8
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D
8,4
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Solution

The correct option is A $$4,8$$
There are two types of closed -packed lattices-

Hexagonal closed packed lattice and Cubic close-packed lattice.
Only FCC lattice forms the cubic closed packed lattice.

So, $$A$$ forms the FCC lattice $$\Rightarrow Z_{eff}=4$$

$$B$$ occupies the tetrahedral voids $$\Rightarrow Z_{eff}=8$$

Therefore, one atom of $$A$$ is surrounded by $$8$$ atoms of $$B$$ and $$B$$ will be surrounded by $$4$$ atoms of $$A$$.

Coordination number of $$A=8$$

Coordination number of $$B=4$$

Therefore, the formula of the compound will be $$A_4B_8$$ Or $$AB_2$$

Hence, the correct option is A. 

Chemistry

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