An ionic compound is made up of A & B only. lons of A occupy all the corners and alternate face centers while that of B occupy body center and edge centers. If B contains -1 charge then charge on atom A will be

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the charge on atom A in the ionic compound made up of ions A and B, we can follow these steps:

### Step 1: Identify the positions of ions A and B
- Ions of A occupy all the corners and alternate face centers.
- Ions of B occupy the body center and edge centers.

### Step 2: Calculate the contribution of ions A
- **Corners:** There are 8 corners in a cube, and each corner contributes \( \frac{1}{8} \) of an ion.
- Contribution from corners = \( 8 \times \frac{1}{8} = 1 \)

- **Alternate face centers:** There are 6 face centers in a cube, but only alternate face centers are occupied by A. Therefore, only 2 face centers contribute.
- Contribution from alternate face centers = \( 2 \times \frac{1}{2} = 1 \)

- **Total contribution from A:**
- Total = Contribution from corners + Contribution from face centers = \( 1 + 1 = 2 \)

### Step 3: Calculate the contribution of ions B
- **Body center:** There is 1 body center which contributes fully.
- Contribution from body center = 1

- **Edge centers:** There are 12 edges in a cube, and each edge center contributes \( \frac{1}{4} \).
- Contribution from edge centers = \( 12 \times \frac{1}{4} = 3 \)

- **Total contribution from B:**
- Total = Contribution from body center + Contribution from edge centers = \( 1 + 3 = 4 \)

### Step 4: Determine the charges
- Given that the charge on B is -1, and there are 4 B ions:
- Total charge from B = \( 4 \times (-1) = -4 \)

### Step 5: Balance the charges
- Let the charge on A be \( x \). Since the compound is neutral, the total charge must equal zero:
\[ \text{Total charge} = \text{Charge from A} + \text{Charge from B} = 0 \]
\[ 2x - 4 = 0 \]

### Step 6: Solve for the charge on A
- Rearranging the equation gives:
\[ 2x = 4 \implies x = \frac{4}{2} = 2 \]

Thus, the charge on atom A is \( +2 \).

### Final Answer:
The charge on atom A is \( +2 \).

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