Problem 19 - A Complete Resource Book in Chemistry for JEE Main

Question

The pattern of successive layers of cep arrangement can be designated as (a) \(\mathrm{AB}, \mathrm{ABC}, \mathrm{AB}, \mathrm{ABC} \ldots\) (b) \(\mathrm{AB}, \mathrm{AB}, \mathrm{AB} \ldots\) (c) \(\mathrm{AB}, \mathrm{BA}, \mathrm{AB}, \mathrm{BA} \ldots\) (d) \(\mathrm{BC}, \mathrm{ABC}, \mathrm{ABC} \ldots\)

Step-by-Step Solution

Answer

Option (b) `AB, AB, AB...` represents hexagonal close packing (hcp).

Step 1: Analyze the Pattern Options

We have four options given for the successive layers of crystal close-packed (ccp) structure arrangement. These options are labeled (a) through (d). Our task is to identify any recognizable repeating pattern or specific sequences seen in real chemistry crystal lattice patterns.

Step 2: Identify Common Patterns in ccp Structures

In crystal structures, common close-packed arrangements include: 1. Hexagonal Close Packing (hcp): which follows an 'ABAB...' sequence. 2. Cubic Close Packing (ccp, also known as face-centered cubic or fcc): which follows an 'ABCABC...' sequence.

Step 3: Examine Each Option

- Option (a) `AB, ABC, AB, ABC...` does not follow a recognized standalone pattern, as it mixes different sequences without consistent repetition. - Option (b) `AB, AB, AB...` corresponds to the sequence for hexagonal close packing (hcp). - Option (c) `AB, BA, AB, BA...` suggests a repeating pattern but does not match any specific recognized model in ccp. - Option (d) `BC, ABC, ABC...` indicates an incorrect sequence mix.

Step 4: Conclusion Based on Analysis

The recognized pattern for hexagonal close packing (hcp) is the one with repeated 'AB' sequences. Thus, option (b) `AB, AB, AB...` best represents the successive layers for the hcp arrangement.

Key Concepts

Close-Packed Structures

In crystallography, close-packed structures are arrangements of atoms where each atom is surrounded by a maximum number of neighbors. This efficient packing minimizes empty space, making these structures incredibly dense. Two primary types of close-packed structures in nature are **Hexagonal Close Packing (HCP)** and **Cubic Close Packing (CCP)**.

These arrangements are commonly found due to their stability and efficiency in using space. In close-packed structures:

• Atoms are considered as hard spheres.
• Each atom touches twelve neighbors.
• The arrangement allows for high packing density.

The efficiency of these structures can be observed in various metals and minerals, where atoms prefer to be as close as possible to minimize energy and maximize space efficiency.

Hexagonal Close Packing

Hexagonal Close Packing (HCP) is a highly efficient arrangement of atoms. Each atom in an HCP structure has a coordination number of 12, meaning it directly contacts 12 other atoms. The distinctive feature of HCP is its repeating layer sequence of **'ABAB...'**.

In this model:

• The first layer is labeled 'A' and the second layer 'B'.
• The third layer is identical to the first, hence 'A', repeating the cycle.

This pattern creates a hexagonal geometry when viewed along the stacking direction.
HCP is prominent in many metals such as cobalt and magnesium, contributing to their specific physical properties.
The geometric configuration of the HCP structure ensures an optimal use of space, which translates to high density and stability under physical stress.

Cubic Close Packing

Cubic Close Packing (CCP), also known as face-centered cubic (FCC), features another efficient close-packing arrangement. Like HCP, each atom in a CCP structure also contacts 12 neighboring atoms.

The CCP structure is characterized by an **'ABCABC...'** stacking sequence:

• Layer 'A' sets the groundwork.
• Layer 'B' is placed on top of 'A', offset so that it fills the dips between 'A' layers.
• Layer 'C', distinct from both 'A' and 'B', continues this offset pattern.

This sequence gives the CCP structure its cubic geometry when observed cubically between layers.
Common metals like aluminum, copper, and gold crystallize in the CCP form. This arrangement facilitates excellent ductility and thermal conductivity properties, useful in various industrial applications. The CCP arrangement is not only structurally efficient but also ideal in properties that favor metallic bonding.