The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)

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The unit cell edge length is $2 \sqrt{2}$ times the radius of the atom

The efficiency of atom packing is 74%

The number of the nearest neightbours of an atom present in the topmost layer is 12

The number of octahedral and tetrachedral voids per atom are 1 and 2, respectively

answer is B, C, D.

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Detailed Solution

CCP is ABC ABC… type packing
(a) In the topmost layer, each atom is in contact with 6 at atoms in same layer and 3 atoms below this layer. Thus, the number, of nearest neighbours is 9.
(b) packing fraction $= \frac{4 \times \frac{4}{3} π r^{3}}{{(\frac{4 r}{\sqrt{2}})}^{3}} = (0.74)$
( c) Each fcc unit has effective no . of atoms = 4
Octahedral void =4
Tetrahedal void =8