In which pair most efficient packing is present ?

Options

A. hcp and bcc
B. hcp and ccp
C. bcc and ccp
D. bcc and simple cubic cell

Explanation

To determine which pair has the most efficient packing, we need to analyze the packing efficiencies of different types of unit cells. Here’s a step-by-step solution:

### Step 1: Understand Packing Efficiency
Packing efficiency refers to the fraction of volume in a crystal structure that is occupied by the constituent particles (atoms, ions, or molecules). It is expressed as a percentage.

### Step 2: Identify the Types of Unit Cells
The common types of unit cells we will consider are:
1. Simple Cubic (SC)
2. Body-Centered Cubic (BCC)
3. Face-Centered Cubic (FCC)
4. Hexagonal Close Packing (HCP)

### Step 3: Calculate Packing Efficiency for Each Unit Cell
- **Simple Cubic (SC)**: Packing efficiency = 52.4%
- **Body-Centered Cubic (BCC)**: Packing efficiency = 68%
- **Face-Centered Cubic (FCC)**: Packing efficiency = 74%
- **Hexagonal Close Packing (HCP)**: Packing efficiency = 74%

### Step 4: Compare the Packing Efficiencies
From the calculated packing efficiencies:
- Simple Cubic: 52.4%
- Body-Centered Cubic: 68%
- Face-Centered Cubic: 74%
- Hexagonal Close Packing: 74%

### Step 5: Identify the Highest Packing Efficiency
The highest packing efficiencies are found in:
- Face-Centered Cubic (FCC) = 74%
- Hexagonal Close Packing (HCP) = 74%

### Conclusion
The pair with the most efficient packing is **FCC and HCP**, both having a packing efficiency of 74%.

### Final Answer
The answer is the pair: **FCC and HCP**.