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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ss072

Which of the following statements about a face-centred cubic lattice of identical atoms (radius $r$ , edge $a$ ) are correct?

A $a = 22 r$ .
BThe distance between nearest neighbours is $a /2$ .
CAbout 26% of the volume is unoccupied.
DThere are 4 atoms per unit cell.

Answer: A, C, D

Corners and faces give

1 + 3 = 4

atoms. Contact is along the face diagonal,

2 a = 4 r

, so

a = 22 r

. The nearest-neighbour distance is half the face diagonal,

a / 2

, not

a /2

. Packing efficiency is 74%, leaving about 26% empty.

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