Fraction of empty space in ABAB type arrangement in 3D

Options

A. 0.74
B. 0.26
C. 0.68
D. 0.32

Answer

To find the fraction of empty space in an ABAB type arrangement in 3D, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding ABAB Arrangement**:
- In an ABAB type arrangement, atoms are arranged in layers, where 'A' and 'B' represent different types of atoms or the same type arranged in a specific manner.

2. **Determine Coordination Number**:
- In this arrangement, the coordination number is the number of nearest neighbors surrounding an atom. For ABAB type arrangement in 3D, the coordination number is 6.

3. **Calculate Packing Fraction**:
- The packing fraction is defined as the volume occupied by the atoms divided by the total volume available. For an ABAB arrangement, the packing fraction is given as 74%. This means that 74% of the volume is occupied by the atoms.

4. **Calculate Fraction of Empty Space**:
- The fraction of empty space can be calculated using the formula:
\[ \text{Fraction of Empty Space} = 1 - \text{Packing Fraction} \]
- Since the packing fraction is 74% (or 0.74 in decimal), we can calculate the fraction of empty space as follows:
\[ \text{Fraction of Empty Space} = 1 - 0.74 = 0.26 \]

5. **Convert to Percentage**:
- To express this fraction as a percentage, we multiply by 100:
\[ \text{Fraction of Empty Space (in percentage)} = 0.26 \times 100 = 26\% \]

6. **Final Answer**:
- Therefore, the fraction of empty space in the ABAB type arrangement in 3D is 0.26.

### Summary:
- The fraction of empty space in an ABAB type arrangement in 3D is **0.26** or **26%**.