The lacttice parameter of `GaAs` (radius of `Ga = 1.22 Å, As = 1.25 Å`) is

Options

A. `5.635 Å`
B. `2.852 Å`
C. `5.774 Å`
D. `4.94 Å`

Explanation

To find the lattice parameter of GaAs, we can follow these steps:

### Step 1: Identify the ionic radii
- The radius of Gallium (Ga) is given as \( r_{Ga} = 1.22 \, \text{Å} \).
- The radius of Arsenic (As) is given as \( r_{As} = 1.25 \, \text{Å} \).

### Step 2: Calculate the radius ratio
- The radius ratio can be calculated using the formula:
\[ \text{Radius Ratio} = \frac{r_{Ga}}{r_{As}} = \frac{1.22 \, \text{Å}}{1.25 \, \text{Å}} = 0.976 \]

### Step 3: Determine the type of structure
- GaAs typically crystallizes in a zinc blende structure, which is a face-centered cubic (FCC) structure.

### Step 4: Calculate the lattice parameter
- In the zinc blende structure, the relationship between the lattice parameter \( a \) and the ionic radii is given by:
\[ a = 2 \sqrt{2} \cdot r_{As} \]
where \( r_{As} \) is the radius of the anion (As).

### Step 5: Substitute the values
- Substitute \( r_{As} = 1.25 \, \text{Å} \) into the equation:
\[ a = 2 \sqrt{2} \cdot 1.25 \, \text{Å} \]

### Step 6: Calculate \( a \)
- Calculate \( a \):
\[ a = 2 \cdot 1.414 \cdot 1.25 \, \text{Å} \approx 3.535 \, \text{Å} \]

### Final Answer
- The lattice parameter of GaAs is approximately \( 3.54 \, \text{Å} \).

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