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Packing refers to the arrangement of con...

Packing refers to the arrangement of constituent units in such a way that the forces of attraction among the constituent particles is the maximum and the contituents occupy the maximum available space. In two dimensions, there are hexagonal close packing and cubic close packing. In three dimentions, there are hexagonal, cubic as well as body centred close packings.
A certain oxide of a metal M crystallises in such a way that `O^(2-)` ions occupy hcp arrangement following ABAB... pattern. The metal ions however occupy `2//3` rd of the octahedral voids. The formula of the compound is :

A

`M_(2)O_(3)`

B

`M_(3)O`

C

`M_(8//3)O_(3)`

D

`MO_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the no. of metal atoms (M) in hcp lattice `=n`
The no. of octahedral voids is the same as the no. of atoms in close packed arrangement
`:.` No of octahedral voids =n
Since only `2//3` of these voids are occupied by metal atoms M
`:.` No of metal atoms in hcp lattice `=(2n)/3`
Ratio of `M:=2 n//3 n=2//3: 1=2:3`
`:.` Formula of metal oxide `=M_(2)O_(3)`
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