In solid X atoms goes to corner of the cube and two alternate face center . Calculate effective number of atom of X in unit cell ?

Answer

To calculate the effective number of atoms of solid X in the unit cell, we can follow these steps:

### Step 1: Identify the positions of the atoms in the unit cell
In solid X, the atoms are located at:
- The corners of the cube
- Two alternate face centers

### Step 2: Count the contribution of corner atoms
There are 8 corners in a cube, and each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell. Therefore, the total contribution from the corner atoms is:
\[ \text{Contribution from corner atoms} = 8 \times \frac{1}{8} = 1 \]

### Step 3: Count the contribution of face-centered atoms
Since there are 2 alternate face centers, and each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell, the total contribution from the face-centered atoms is:
\[ \text{Contribution from face-centered atoms} = 2 \times \frac{1}{2} = 1 \]

### Step 4: Calculate the effective number of atoms in the unit cell
Now, we can add the contributions from the corner atoms and the face-centered atoms to find the effective number of atoms (Z) in the unit cell:
\[ Z = \text{Contribution from corner atoms} + \text{Contribution from face-centered atoms} = 1 + 1 = 2 \]

### Final Answer
The effective number of atoms of X in the unit cell is \( \mathbf{2} \).

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