An ionic compound is formed between a metal M and a non-metal Y. If M occupies half the octahedral voids in the cubic close-packed arrangement formed by Y, the chemical formula of the ionic compound is

Options

A. MY
B. `MY_2`
C. `M_2Y`
D. `MY_3`

Explanation

To determine the chemical formula of the ionic compound formed between the metal M and the non-metal Y, we can follow these steps:

### Step 1: Understand the arrangement of non-metal Y
In a cubic close-packed (ccp) structure, also known as face-centered cubic (fcc), the non-metal Y occupies the corners and the face centers of the unit cell.

### Step 2: Calculate the number of Y atoms in the unit cell
- The contribution from the corner atoms: There are 8 corners in a cube, and each corner atom is shared by 8 unit cells. Therefore, the contribution from the corners is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]
- The contribution from the face-centered atoms: There are 6 faces, and each face atom is shared by 2 unit cells. Therefore, the contribution from the face centers is:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]
- Total number of Y atoms in the unit cell:
\[ \text{Total Y atoms} = 1 + 3 = 4 \text{ atoms} \]

### Step 3: Determine the number of octahedral voids in the unit cell
In a cubic close-packed structure, the number of octahedral voids is equal to the number of atoms in the unit cell. Since we have 4 Y atoms, there are also 4 octahedral voids.

### Step 4: Find the number of metal M atoms
According to the problem, metal M occupies half of the octahedral voids. Therefore, the number of M atoms is:
\[ \text{Number of M atoms} = \frac{4}{2} = 2 \text{ atoms} \]

### Step 5: Write the chemical formula
Now we can write the chemical formula based on the number of atoms of M and Y:
- Number of Y atoms = 4
- Number of M atoms = 2

Thus, the chemical formula of the ionic compound is:
\[ \text{M}_2\text{Y}_4 \]
This can be simplified to:
\[ \text{MY}_2 \]

### Final Answer
The chemical formula of the ionic compound is **MY₂**.

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