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In a cubic lattice, the close packed str...

In a cubic lattice, the close packed structure of mixed oxides of the lattice is made up of oxide ion, one eighth of the tetrahedral voids are occupied by divalent ions `(X^(2+))` while one half of the octahedral voids are occupied by trivalent ions `(Y^(3+))`. What is the formula of the oxide?

Text Solution

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Let there be n number of `O^(2-)` in the crystal.
`therefore` Number of octahedral voids = n
Number of tetrahedral voids = 2n
`X^(2+)"ions"=1/8xx2n=n/4" "Y^(3+)"ions"=1/2xxn=n/2`
`O^(2-)"ions"=1/8xx8=1" "X^(2+):Y^(3+):O^(2-)=n/4:n/2:n`
Therefore, formula of the oxide = `XY_(2)O_(4)`.
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