Total no. of voids in `0.5` mole of a compound forming hexagonal closed packed structure are :

Options

A. `6.022xx10^(23)`
B. `3.011xx10^(23)`
C. `9.033xx10^(23)`
D. `4.516xx10^(23)`

Explanation

To find the total number of voids in 0.5 moles of a compound forming a hexagonal closed packed (HCP) structure, we can follow these steps:

### Step 1: Determine the number of atoms in 0.5 moles of the compound.
- The number of atoms in one mole of a substance is given by Avogadro's number, which is approximately \(6.022 \times 10^{23}\).
- Therefore, the number of atoms in 0.5 moles is calculated as:
\[ \text{Number of atoms} = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23} \]

### Step 2: Find the number of unit cells.
- In a hexagonal close packed structure, there are 6 atoms per unit cell.
- To find the total number of unit cells, we divide the total number of atoms by the number of atoms per unit cell:
\[ \text{Number of unit cells} = \frac{3.011 \times 10^{23}}{6} = 5.018 \times 10^{22} \]

### Step 3: Calculate the number of voids in the unit cell.
- In HCP, there are 6 octahedral voids and 12 tetrahedral voids per unit cell.
- Therefore, the total number of voids per unit cell is:
\[ \text{Total voids per unit cell} = \text{Octahedral voids} + \text{Tetrahedral voids} = 6 + 12 = 18 \]

### Step 4: Calculate the total number of voids in the given moles.
- To find the total number of voids in the total number of unit cells, we multiply the number of unit cells by the total voids per unit cell:
\[ \text{Total voids} = \text{Number of unit cells} \times \text{Total voids per unit cell} = 5.018 \times 10^{22} \times 18 \]
- Calculating this gives:
\[ \text{Total voids} = 9.033 \times 10^{23} \]

### Conclusion
Thus, the total number of voids in 0.5 moles of a compound forming a hexagonal closed packed structure is \(9.033 \times 10^{23}\).

### Final Answer
The answer is \(9.033 \times 10^{23}\) (Option C).

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