A compound forms hexagonal close packed structure. What is the total number of voids in 0.5 mol of it.

Options

A. `9 xx 10^23 `
B. `6 xx 10^23`
C. `3 xx 10^23 `
D. `1.8 xx 10^23`

Explanation

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

### Step 1: Determine the number of particles in 0.5 moles
We know that 1 mole of any substance contains Avogadro's number of particles, which is approximately \(6.02 \times 10^{23}\).

For 0.5 moles:
\[ \text{Number of particles} = 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \]

### Step 2: Calculate the number of octahedral voids
In an HCP structure, the number of octahedral voids is equal to the number of particles present in the lattice. Therefore, the number of octahedral voids in 0.5 moles is:
\[ \text{Number of octahedral voids} = 3.01 \times 10^{23} \]

### Step 3: Calculate the number of tetrahedral voids
The number of tetrahedral voids in an HCP structure is twice the number of octahedral voids. Thus:
\[ \text{Number of tetrahedral voids} = 2 \times \text{Number of octahedral voids} = 2 \times 3.01 \times 10^{23} = 6.02 \times 10^{23} \]

### Step 4: Calculate the total number of voids
The total number of voids is the sum of octahedral and tetrahedral voids:
\[ \text{Total voids} = \text{Number of octahedral voids} + \text{Number of tetrahedral voids} \]
\[ \text{Total voids} = 3.01 \times 10^{23} + 6.02 \times 10^{23} = 9.03 \times 10^{23} \]

### Step 5: Final answer
Thus, the total number of voids in 0.5 moles of the compound is:
\[ \text{Total voids} \approx 9.03 \times 10^{23} \text{ (or approximately } 9 \times 10^{23}\text{)} \]