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JEE Advanced levelSingle correct optionDifficulty 3 of 3ss049

In a crystal, atoms A form an fcc lattice, atoms B occupy three-quarters of the tetrahedral voids and atoms C occupy half of the octahedral voids. The simplest formula is

A $A X_{4} B X_{6} C X_{2}$
B $A X_{2} B X_{3} C$
C $AB X_{3} C X_{2}$
D $A X_{3} B X_{2} C$

Answer: B

Per unit cell A

= 4

; tetrahedral voids

= 8

, so B

= \frac{3}{4} \times 8 = 6

; octahedral voids

= 4

, so C

= \frac{1}{2} \times 4 = 2

. Ratio

4 : 6 : 2 = 2 : 3 : 1

, so the simplest formula is

A X_{2} B X_{3} C

.

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