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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ss043

Anions X form a ccp lattice containing $N$ anions. Cations A occupy some of the voids. Which of the following formula assignments are correct?

AAll tetrahedral voids occupied: $A X_{2} X$
BHalf of the octahedral voids occupied: $AX$
COne-third of the tetrahedral voids occupied: $A X_{2} X X_{3}$
DOne-quarter of the octahedral voids occupied: $A X_{4} X$

Answer: A, C

There are

N

octahedral and

2 N

tetrahedral voids. All tetrahedral voids:

A = 2 N

, formula

A X_{2} X

. Half of octahedral:

A = N /2

, giving

AX X_{2}

. One-third of tetrahedral:

A = 2 N /3

, giving

A X_{2} X X_{3}

. One-quarter of octahedral:

A = N /4

, giving

AX X_{4}

.

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