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Question

# In a cubic packed structure of mixed oxides, the lattice is made up of oxide ions, one-fifth of tetrahedral voids are occupied by X ion while half of the octahedral voids are occupied by Y ion. What will be the formula of oxide mixture?

A
X5Y4O10
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B
X4Y5O10
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C
XY2O4
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D
X2YO4
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Solution

## The correct option is B X4Y5O10 The given oxide mixture is in cubic closed packing, where the lattice is made of oxide ion. ∴ Number of O2−ions in the unit cell =n Number of tetrahedral voids =2n Number of octahedral voids =n Here, X ion occupies one-fifth of tetrahedral voids. Thus, Number of X ion =2n5 Also, Y ion occupies half of the octahedral voids. Thus, Number of Y ion =n2 X:Y:O2n5:n2:n4:5:10⎫⎪ ⎪ ⎪⎬⎪ ⎪ ⎪⎭Simplest formula=X4Y5O10

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