The correct order of the packing efficiency in different types of unit cells is

Options

A. `"fcc" lt "bcc" lt "simple cubic"`
B. `"fcc" gt "bcc" gt "simple cubic"`
C. `"fcc" lt "bcc" gt "simple cubic"`
D. `"bcc" lt "fcc" gt "simple cubic"`

Explanation

To determine the correct order of packing efficiency in different types of unit cells (FCC, BCC, and simple cubic), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Packing Efficiency**:
- Packing efficiency is defined as the percentage of the total volume of a unit cell that is occupied by the constituent particles (atoms, ions, or molecules). It is calculated using the formula:
\[ \text{Packing Efficiency} = \left( \frac{\text{Volume of particles in the unit cell}}{\text{Volume of the unit cell}} \right) \times 100 \]

2. **Identify the Types of Unit Cells**:
- The three types of unit cells we are considering are:
- Simple Cubic (SC)
- Body-Centered Cubic (BCC)
- Face-Centered Cubic (FCC)

3. **Calculate Packing Efficiency for Each Unit Cell**:
- **Simple Cubic (SC)**:
- Contains 1 atom per unit cell.
- Packing efficiency = 52%
- **Body-Centered Cubic (BCC)**:
- Contains 2 atoms per unit cell.
- Packing efficiency = 68%
- **Face-Centered Cubic (FCC)**:
- Contains 4 atoms per unit cell.
- Packing efficiency = 74%

4. **Arrange the Packing Efficiencies**:
- Now, we can arrange the packing efficiencies calculated:
- FCC: 74%
- BCC: 68%
- SC: 52%

5. **Determine the Correct Order**:
- From the above calculations, the order of packing efficiency from highest to lowest is:
- FCC > BCC > Simple Cubic

6. **Final Answer**:
- The correct order of packing efficiency in different types of unit cells is:
- FCC > BCC > Simple Cubic