Which of the following is correct order of packing efficiency?

Options

A. `HCP=F C C gt B C C gt SC`
B. `SC gt B C C gt HCP=F CC `
C. `B C Cgt SC gt HCP lt F C C`
D. `F C C=HCP gt SC gt B C C`

Explanation

To determine the correct order of packing efficiency among different crystal structures, we need to know the packing efficiencies of each type of packing. Here’s the step-by-step solution:

### Step 1: Identify the Types of Packing
The types of packing we need to consider are:
- HCP (Hexagonal Close Packing)
- FCC (Face-Centered Cubic)
- BCC (Body-Centered Cubic)
- SC (Simple Cubic)

### Step 2: Know the Packing Efficiencies
Next, we need to know the packing efficiencies for each of these structures:
- **HCP**: Packing efficiency = 74%
- **FCC**: Packing efficiency = 74%
- **BCC**: Packing efficiency = 68%
- **SC**: Packing efficiency = 52%

### Step 3: Compare the Packing Efficiencies
Now, we can compare the packing efficiencies:
- HCP and FCC both have the same packing efficiency of 74%.
- BCC has a packing efficiency of 68%.
- SC has the lowest packing efficiency of 52%.

### Step 4: Arrange in Order of Packing Efficiency
Based on the packing efficiencies, we can arrange them in the following order:
1. HCP = FCC (74%)
2. BCC (68%)
3. SC (52%)

Thus, the correct order of packing efficiency is:
HCP = FCC > BCC > SC

### Step 5: Choose the Correct Option
Now, we can look at the options provided in the question. The correct option that matches our derived order is:
- **Option 1**: HCP = FCC > BCC > SC

### Final Answer
The correct order of packing efficiency is:
**HCP = FCC > BCC > SC**

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