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JEE Advanced levelSingle correct optionDifficulty 3 of 3ss158

A cubic unit cell has atoms $Z$ at six corners and atoms $W$ at the two remaining corners (adjacent along one edge). Atoms $X$ are at the centres of all six faces. The formula of the compound is

A $Z X_{6} WX X_{3}$
B $ZWX X_{3}$
C $Z X_{3} WX X_{12}$
D $Z X_{3} W X_{2} X X_{12}$

Answer: C

Z = 6 \times \frac{1}{8} = \frac{3}{4}

;

W = 2 \times \frac{1}{8} = \frac{1}{4}

;

X = 6 \times \frac{1}{2} = 3

. The ratio

\frac{3}{4} : \frac{1}{4} : 3 = 3 : 1 : 12

, hence

Z X_{3} WX X_{12}

.

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