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 fractions of the different types of crystal structures mentioned in the question. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Packing Fraction
The packing fraction is a measure of how efficiently the particles (atoms, ions, or molecules) are packed in a crystal structure. It is defined as the ratio of the volume occupied by the particles to the total volume of the unit cell. A higher packing fraction indicates more efficient packing.

### Step 2: Identify Packing Fractions of Different Structures
We need to know the packing fractions for the given crystal structures:
- Simple Cubic Packing (SCP): Packing fraction = 74%
- Cubic Close Packing (CCP): Packing fraction = 74%
- Body-Centered Cubic (BCC): Packing fraction = 68%
- Simple Cubic Cell: Packing fraction = 54%

### Step 3: Analyze the Pairs
Now, we will analyze each pair provided in the options to find which has the highest packing fraction:
1. **SCP and BCC**:
- SCP = 74%
- BCC = 68%
- Average packing fraction = (74% + 68%) / 2 = 71%

2. **SCP and CCP**:
- SCP = 74%
- CCP = 74%
- Average packing fraction = (74% + 74%) / 2 = 74%

3. **BCC and CCP**:
- BCC = 68%
- CCP = 74%
- Average packing fraction = (68% + 74%) / 2 = 71%

4. **BCC and Simple Cubic Cell**:
- BCC = 68%
- Simple Cubic Cell = 54%
- Average packing fraction = (68% + 54%) / 2 = 61%

### Step 4: Determine the Most Efficient Pair
From the calculations:
- SCP and BCC: 71%
- SCP and CCP: 74%
- BCC and CCP: 71%
- BCC and Simple Cubic Cell: 61%

The pair with the highest packing fraction is **SCP and CCP**, both having a packing fraction of 74%.

### Conclusion
Thus, the pair with the most efficient packing is **SCP and CCP**.

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