The correct statement (s) for cubic close packed (ccp) three dimensional structure are:
(A) The number of the neighbours of an atom present in the top most layer is \(12\).
(B) The efficiency of atom packing is \(74\%\).
(C) The number of octahedral and tetrahedral voids per atom are \(1\) & \(2\), respectively.
(D) The unit cell edge length is \(2\sqrt{2}\) times the radius of the atom.
(E) The metals like Be, Cd, Mg, Zn have cubic close packed (ccp) structure.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (B), (C) and (D) Only
In cubic close packing (ccp, the same as fcc) the third layer covers the octahedral voids of the second, giving the ABCABC pattern. Each atom inside the crystal touches 12 others, the spheres fill 74% of the space, and N close-packed spheres create N octahedral and 2N tetrahedral voids.
(A) The number of the neighbours of an atom present in the top most layer is \(12\). — False. An atom inside the crystal has 12 neighbours: 6 in its own layer, 3 above and 3 below. An atom in the top-most layer has no layer above it, so it has only 6 + 3 = 9 neighbours.
(B) The efficiency of atom packing is \(74\%\). — True. Both ccp and hcp are the most efficient packings: 74% of the space is filled and 26% is empty.
(C) The number of octahedral and tetrahedral voids per atom are \(1\) & \(2\), respectively. — True. For N atoms there are N octahedral and 2N tetrahedral voids, that is 1 and 2 per atom.
(D) The unit cell edge length is \(2\sqrt{2}\) times the radius of the atom. — True. In an fcc unit cell the atoms touch along the face diagonal, so the face diagonal is 4r. It is also \( \sqrt{2}\,a \):
\( \displaystyle \sqrt{2}\,a = 4r \quad \Rightarrow \quad a = \frac{4r}{\sqrt{2}} = 2\sqrt{2}\,r \)
(E) The metals like Be, Cd, Mg, Zn have cubic close packed (ccp) structure. — False. These metals crystallise in the hcp (hexagonal close packed, ABAB) structure, not ccp. Copper and silver are examples of ccp metals.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic is not there in the latest NCERT book (2026-27), and it is also out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Placing Third Layer over the Second Layer – …
Placing Third Layer over the Second Layer – …
Formula of a Compound and Number of Voids Filled
