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 :

(B), (C) and (D) Only

The correct answer is option 1. (B), (C) and (D) Only.

The cubic close packed (CCP) structure is a highly efficient way for atoms to pack together in a three-dimensional crystal lattice. Let's break down the statements you mentioned and explain why some are true and others are not:

Statement (A) The number of the neighbours of an atom present in the top most layer is \(12\): False

An atom in the topmost layer of a CCP structure has only 6 nearest neighbors, not 12. The 12 neighbors are for an atom located in the middle of the unit cell, where it's surrounded by atoms from all sides. The topmost layer atoms only have contact with atoms below them and those on the sides, forming a hexagonal pattern.

Statement (B) The efficiency of atom packing is \(74\%\): True

The packing efficiency in CCP is about 74%. This means 74% of the available space in the unit cell is occupied by atoms. This is a relatively high packing efficiency compared to other structures like simple cubic (52%).

Statement (C) The number of octahedral and tetrahedral voids per atom are \(1\) & \(2\), respectively: True

A CCP structure has two distinct types of voids (empty spaces) between the atoms:

Octahedral voids: There is one octahedral void per atom. This void is located at the center of a cube formed by eight atoms.

Tetrahedral voids: There are two tetrahedral voids per atom. These voids are located in between four atoms arranged in a tetrahedral shape.

Visualizing Voids: Imagine the atoms in a CCP structure as spheres. The octahedral void is like a larger sphere nestled in the center of eight smaller spheres. The tetrahedral voids are smaller spaces created by four spheres arranged in a pyramid shape.

Statement (D) The unit cell edge length is \(2\sqrt{2}\) times the radius of the atom: True

The unit cell edge length (a) in a CCP structure is related to the atomic radius (r) by the formula: \(a = \frac{4r}{\sqrt{2}}\)This can be rearranged to: \(a = 2\sqrt{2}r\)Therefore, the unit cell edge length is indeed \(a = 2\sqrt{2}\) times the radius of the atom.

Statement (E) The metals like Be, Cd, Mg, Zn have cubic close packed (ccp) structure: False

Explanation: Beryllium (Be), Cadmium (Cd), Magnesium (Mg), and Zinc (Zn) are some examples of metals that can adopt a CCP structure. However, it's important to note that not all these metals will have a CCP structure exclusively. The specific structure a metal adopts depends on various factors like atomic size and electron configuration.

Additional points to consider: CCP is one of the two most common close-packed structures, the other being hexagonal close packed (HCP).

CCP structures are often favored by metals due to their high packing efficiency and stability.