The percentages of void space for simple cubic, body centred cubic and hexagonal close packed arranged respectively are

Options

A. 48, 32, 26
B. 48, 26, 32
C. 26, 48, 32
D. 32, 48, 26

Answer

To find the percentages of void space for simple cubic, body-centered cubic, and hexagonal close-packed structures, we will first determine the packing efficiency for each type of structure and then calculate the void space.

### Step-by-Step Solution:

1. **Simple Cubic Structure:**
- The packing efficiency of a simple cubic structure is approximately **52.36%**.
- To find the void space, we subtract the packing efficiency from 100%:
\[ \text{Void Space} = 100\% - \text{Packing Efficiency} = 100\% - 52.36\% = 47.64\% \]
- We can round this to **48%**.

2. **Body-Centered Cubic Structure:**
- The packing efficiency of a body-centered cubic structure is approximately **68%**.
- To find the void space, we again subtract the packing efficiency from 100%:
\[ \text{Void Space} = 100\% - \text{Packing Efficiency} = 100\% - 68\% = 32\% \]

3. **Hexagonal Close-Packed Structure:**
- The packing efficiency of a hexagonal close-packed structure is approximately **74%**.
- To find the void space, we perform the same calculation:
\[ \text{Void Space} = 100\% - \text{Packing Efficiency} = 100\% - 74\% = 26\% \]

### Final Result:
The percentages of void space for the three structures are:
- Simple Cubic: **48%**
- Body-Centered Cubic: **32%**
- Hexagonal Close-Packed: **26%**

Thus, the final answer is **48%, 32%, and 26%** respectively.

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