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 Gallium Arsenide (GaAs), we will follow these steps:

### Step 1: Understand the relationship between atomic radii and lattice parameter
In a BCC (Body-Centered Cubic) lattice, the relationship between the atomic radii (R) of the two different atoms (Ga and As) and the lattice parameter (a) can be expressed using the formula:
\[ \sqrt{3}a = 4R \]
Where \( R \) is the effective radius calculated as:
\[ R = R_{Ga} + R_{As} \]

### Step 2: Calculate the effective radius
Given:
- Radius of Ga (R_Ga) = 1.22 Å
- Radius of As (R_As) = 1.25 Å

We can calculate the effective radius \( R \):
\[ R = R_{Ga} + R_{As} = 1.22 + 1.25 = 2.47 \, \text{Å} \]

### Step 3: Substitute into the formula
Now, substituting the value of \( R \) into the equation for the lattice parameter:
\[ \sqrt{3}a = 4R \]
\[ \sqrt{3}a = 4 \times 2.47 \]

### Step 4: Calculate the right-hand side
Calculating the right-hand side:
\[ 4 \times 2.47 = 9.88 \]

### Step 5: Solve for the lattice parameter 'a'
Now, we can solve for 'a':
\[ a = \frac{9.88}{\sqrt{3}} \]

Calculating \( \sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]
Thus,
\[ a = \frac{9.88}{1.732} \approx 5.70 \, \text{Å} \]

### Step 6: Finalize the answer
After calculating, we find that the lattice parameter \( a \) for GaAs is approximately:
\[ a \approx 5.70 \, \text{Å} \]

### Summary
The lattice parameter of GaAs is approximately 5.70 Å.

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