The tetrahedral voids are present in 0.5 mole of hcp crystal structure.

Options

A. `3.6xx10^(23)`
B. `9xx10^(23)`
C. `3.6xx10^(24)`
D. `6.02xx10^(23)`

Explanation

To solve the problem of determining the number of tetrahedral voids in 0.5 mole of HCP (hexagonal close-packed) crystal structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the HCP Structure**:
- In an HCP unit cell, there are a total of 6 atoms.

2. **Calculate the Number of Tetrahedral Voids**:
- The number of tetrahedral voids in a crystal structure is given by the formula:
\[ \text{Number of tetrahedral voids} = 2 \times \text{Number of atoms in the unit cell} \]
- For HCP, substituting the number of atoms:
\[ \text{Number of tetrahedral voids} = 2 \times 6 = 12 \]
- Thus, one HCP unit cell contains 12 tetrahedral voids.

3. **Determine the Number of Moles of Tetrahedral Voids in 0.5 Mole of HCP**:
- Since one mole of HCP contains 12 moles of tetrahedral voids, we can calculate for 0.5 mole:
\[ \text{Tetrahedral voids in 0.5 mole HCP} = 12 \times 0.5 = 6 \text{ moles} \]

4. **Convert Moles of Tetrahedral Voids to Number of Voids**:
- To find the actual number of tetrahedral voids, we multiply the number of moles by Avogadro's number (\(6.022 \times 10^{23}\)):
\[ \text{Number of tetrahedral voids} = 6 \times 6.022 \times 10^{23} \approx 3.6132 \times 10^{24} \]

5. **Final Result**:
- Therefore, the number of tetrahedral voids in 0.5 mole of HCP is approximately \(3.6 \times 10^{24}\).