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What is the simplest formula of a solid ...

What is the simplest formula of a solid whose unit cell has the atom A at each corner, the atom B at each face centre and a atom C at the body centre.

A

`A_(2)BC`

B

`AB_(2)C`

C

`AB_(3)C`

D

`ABC_(2)`

Text Solution

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An atom at the corner of a cube is shared among it unit cells. As there are 8 corners in a cube, number of corner atom (A) per unit cell `=8((1)/(8))=1`
A face-centred atom in a cube is shared by two unit cells. As there are 6 faces in a cube, number of face-centred atoms (B) per unit cell `=6xx(1)/(2)=3`.
An atom in the body of the cube is not shared by other cells.
`therefore` Number of atoms (C) at the body centre per unit cell=1.
Hence (C), the formula of the solid is `AB_(2)C`.
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