Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The coordination number of a metal crystallizing in a hexagonal close-packed structure is (a) 12 (b) 4 (c) 8 (d) 6

Step-by-Step Solution

Answer

The coordination number is 12.

Step 1: Define Coordination Number

The coordination number of an atom in a crystal lattice is the number of nearest neighbor atoms that surround it. For metals crystallizing in close-packed structures, this concept determines the metal's stability and packing efficiency.

Step 2: Introduce Hexagonal Close-Packed (hcp) Structure

In the hcp structure, atoms are packed as closely as possible. This structure consists of three layers where the atoms in each layer are arranged such that they touch neighboring atoms, contributing to its high packing efficiency.

Step 3: Examine Atom Arrangement in hcp

The hcp structure can be visualized as consisting of two types of layers (denoted as A and B) stacked in an ABAB sequence. In one layer (A), each atom is surrounded by six others in the same plane to form a hexagon.

Step 4: Count the Number of Nearest Neighbors

For each atom in the hcp structure, it has 6 nearest neighbors in the same layer, 3 neighbors in the layer above, and 3 neighbors in the layer below. Thus, the total number of nearest neighbors is 12.

Step 5: Determine the Coordination Number

Considering all the nearest neighbors, the coordination number for an atom in a hcp structure is computed as follows: \(6 + 3 + 3 = 12\). Hence, the coordination number of atoms in hcp is 12.

Key Concepts

Hexagonal Close-Packed Structure

The hexagonal close-packed (hcp) structure is a fascinating arrangement seen in some metals, like zinc and magnesium. Imagine stacking oranges in a grocery store. The layers are organized tightly, allowing no gaps. Similarly, in the hcp structure, atoms are packed as closely as possible.

The arrangement is not random, though. It follows an ABAB pattern, where each layer shifts to nestle into the spaces of the layer below. This creates a repeating pattern offering maximum stability and strength.

• Atoms in the same layer form a hexagon, a shape known for its efficiency and tessellation abilities.
• The ABAB stacking ensures that despite being packed tightly, each atom enjoys the maximum possible connection with its neighbors.

This meticulous pattern is the secret behind the hcp structure's stability and impressive packing efficiency.

Crystal Lattice

A crystal lattice is a beautifully ordered array of atoms, ions, or molecules. This regular arrangement forms the backbone of many solid structures in the natural world.

In the case of the hcp structure, we have a special type of lattice. Lattices in this structure look like stacked layers of hexagons. Imagine the artistic work behind a honeycomb—we see a similar elegant symmetry.

• In an hcp lattice, each layer is a repeating hexagon pattern where each atom is surrounded by six others in its plane.
• Such layers alternate, ensuring that every atom is ideally positioned relative to its neighbors in adjacent layers.

This coordination and repetition define the crystal lattice's stability and the material's characteristics, influencing both density and strength.

Packing Efficiency

Packing efficiency is a key concept in understanding how densely atoms or molecules are packed in a structure. In the hcp structure, this efficiency is remarkably high due to the smart arrangement of atoms.

When we say something has high packing efficiency, we're saying how much of the available space is actually filled by atoms, as opposed to being empty space. For hcp, this is achieved through its ABAB stacking pattern.

• The arrangement allows atoms to be as close together as physics allows without additional empty spaces.
• This maximized contact between atoms translates to material that is dense and robust.

The packing efficiency of hcp and its close relation, the face-centered cubic (fcc), is around 74%. This high percentage evidences the material's optimal use of space, resulting in some of the most stable crystal structures found in nature.