An ionic solid consists of A atoms and B atoms, and its unit cell structure is shown below. The position of A atoms (orange color) and the position of B atoms (blue color) in the cubic unit cell are indicated in the picture. Based on the cubic unit cell given here, which statement is correct? A= edge B=comer, center O a. The empirical formula of this ionic compound is A12B5. O b. The empirical formula of this ionic compound is A3B2. O. The empirical formula of this ionic compound is A2B3. d. The empirical formula of this ionic compound is AB3. e. None of the above

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Chapter1: Chemical Foundations
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**Unit Cell Analysis of Ionic Compound**

An ionic solid consists of A atoms and B atoms, and its unit cell structure is shown below. The position of A atoms (orange color) and the position of B atoms (blue color) in the cubic unit cell are indicated in the picture.

Based on the cubic unit cell given here, which statement is correct?

**Diagram Explanation:**

- **A atoms (orange)**: Positioned at the edges of the cube.
- **B atoms (blue)**: Positioned at the corners and the center of the cube.

**Options:**

- a. The empirical formula of this ionic compound is A₁₂B₅.
- b. The empirical formula of this ionic compound is A₃B₂.
- c. The empirical formula of this ionic compound is A₂B₃.
- d. The empirical formula of this ionic compound is AB₃.
- e. None of the above

**Visual Analysis:**

In the diagram:

- Each edge contains one A atom, and there are 12 edges in total. However, each edge atom is shared by 4 cells, so effectively 3 A atoms per unit cell.
- B atoms are at all the corners and the center. There are 8 corners (1/8 contribution each) plus 1 full atom at the center, totaling effectively 2 B atoms.

**Correct Answer:**

b. The empirical formula of this ionic compound is A₃B₂.
Transcribed Image Text:**Unit Cell Analysis of Ionic Compound** An ionic solid consists of A atoms and B atoms, and its unit cell structure is shown below. The position of A atoms (orange color) and the position of B atoms (blue color) in the cubic unit cell are indicated in the picture. Based on the cubic unit cell given here, which statement is correct? **Diagram Explanation:** - **A atoms (orange)**: Positioned at the edges of the cube. - **B atoms (blue)**: Positioned at the corners and the center of the cube. **Options:** - a. The empirical formula of this ionic compound is A₁₂B₅. - b. The empirical formula of this ionic compound is A₃B₂. - c. The empirical formula of this ionic compound is A₂B₃. - d. The empirical formula of this ionic compound is AB₃. - e. None of the above **Visual Analysis:** In the diagram: - Each edge contains one A atom, and there are 12 edges in total. However, each edge atom is shared by 4 cells, so effectively 3 A atoms per unit cell. - B atoms are at all the corners and the center. There are 8 corners (1/8 contribution each) plus 1 full atom at the center, totaling effectively 2 B atoms. **Correct Answer:** b. The empirical formula of this ionic compound is A₃B₂.
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