In a body-centred cubic arrangement the ion A occupies the centre while the ions of B occupy the corners of a cube. The formula of the crystal is:

Options

A. AB
B. `A_(2)B`
C. `AB_(2)`
D. `AB_(3)`

Answer

To determine the formula of the crystal in a body-centered cubic arrangement where ion A occupies the center and ions of B occupy the corners of the cube, we can follow these steps:

### Step 1: Identify the number of ions at the corners
In a cube, there are 8 corners. Each corner ion (B) contributes 1/8 of an ion to the unit cell because each corner is shared by 8 adjacent cubes.

**Calculation:**
Number of B ions contributed by corners = 8 corners × (1/8 contribution per corner) = 1 B ion.

### Step 2: Identify the number of ions in the center
In a body-centered cubic (BCC) structure, there is 1 ion (A) located at the center of the cube.

### Step 3: Combine the contributions
Now, we combine the contributions from both types of ions:
- From the corners: 1 B ion
- From the center: 1 A ion

### Step 4: Write the formula
The formula of the crystal can be expressed as:
- A (from the center) and B (from the corners) combine to give the formula AB.

### Final Answer:
The formula of the crystal is **AB**.

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