In ccp, ratio of no. of atoms to no. of tetrahedral void is -

Options

A. `(1)/(1)`
B. `(2)/(1)`
C. `(0.5)/(1)`
D. `(3)/(1)`

Answer

To find the ratio of the number of atoms to the number of tetrahedral voids in a cubic close-packed (CCP) structure, we can follow these steps:

### Step 1: Understand the Structure
CCP refers to the cubic close-packed structure, which is also known as face-centered cubic (FCC). In this structure, atoms are located at the corners and the centers of the faces of the cube.

### Step 2: Calculate the Number of Atoms in the Unit Cell
In an FCC unit cell:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell. Therefore, from the corners:
\[ \text{Atoms from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom to the unit cell. Therefore, from the faces:
\[ \text{Atoms from faces} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]
- Total number of atoms in the FCC unit cell:
\[ \text{Total atoms} = 1 + 3 = 4 \text{ atoms} \]

### Step 3: Calculate the Number of Tetrahedral Voids
In a close-packed structure, the number of tetrahedral voids is given by:
\[ \text{Number of tetrahedral voids} = 2n \]
where \( n \) is the number of atoms in the unit cell. Since we found \( n = 4 \):
\[ \text{Tetrahedral voids} = 2 \times 4 = 8 \text{ voids} \]

### Step 4: Calculate the Ratio
Now, we can calculate the ratio of the number of atoms to the number of tetrahedral voids:
\[ \text{Ratio} = \frac{\text{Number of atoms}}{\text{Number of tetrahedral voids}} = \frac{4}{8} = \frac{1}{2} \]

### Conclusion
The ratio of the number of atoms to the number of tetrahedral voids in a cubic close-packed structure is \( \frac{1}{2} \).

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