Empty space in ccp lattice is

Options

A. `26%`
B. `45%`
C. `90%`
D. `30%`

Explanation

To determine the empty space in a cubic close-packed (ccp) lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Packing Efficiency**:
- The packing efficiency of a crystal lattice is defined as the fraction of the volume occupied by the spheres (atoms) in the lattice compared to the total volume of the lattice.

2. **Determine the Number of Atoms in CCP**:
- In a cubic close-packed (ccp) structure, there are 4 atoms per unit cell.

3. **Volume of a Sphere**:
- The volume \( V \) of a single sphere (atom) is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]

4. **Total Volume Occupied by Atoms in CCP**:
- The total volume occupied by the 4 atoms in the unit cell is:
\[ \text{Total Volume} = 4 \times \frac{4}{3} \pi r^3 = \frac{16}{3} \pi r^3 \]

5. **Edge Length of the Unit Cell**:
- For a ccp lattice, the edge length \( a \) is related to the radius \( r \) of the spheres by the formula:
\[ a = \frac{4r}{\sqrt{2}} \]

6. **Total Volume of the Unit Cell**:
- The volume of the cubic unit cell is:
\[ \text{Volume of Unit Cell} = a^3 = \left(\frac{4r}{\sqrt{2}}\right)^3 = \frac{64r^3}{2\sqrt{2}} = 32\sqrt{2} r^3 \]

7. **Calculating Packing Efficiency**:
- The packing efficiency can now be calculated using the formula:
\[ \text{Packing Efficiency} = \left(\frac{\text{Volume Occupied by Atoms}}{\text{Volume of Unit Cell}}\right) \times 100 \]
- Substituting the values:
\[ \text{Packing Efficiency} = \left(\frac{\frac{16}{3} \pi r^3}{32\sqrt{2} r^3}\right) \times 100 \]
- Simplifying this gives:
\[ \text{Packing Efficiency} = \left(\frac{16\pi}{96\sqrt{2}}\right) \times 100 = \frac{16\pi \times 100}{96\sqrt{2}} \approx 74\% \]

8. **Finding the Empty Space**:
- The empty space in the ccp lattice can be calculated as:
\[ \text{Empty Space} = 100\% - \text{Packing Efficiency} \]
- Therefore:
\[ \text{Empty Space} = 100\% - 74\% = 26\% \]

### Final Answer:
The empty space in a cubic close-packed (ccp) lattice is **26%**.