A compound contains atoms X,Y and Z. the oxidation number of X is `+2`, of Y is `+5` and of Z is `-2`. The possible formula of the compound is

Options

A. `XYZ_(2)`
B. `Y_(2)(XZ_(3))_(2)`
C. `X_(3)(YZ_(4))_(2)`
D. `X_(3)(Y_(4)Z)_(2)`

Explanation

To determine the possible formula of the compound containing atoms X, Y, and Z with given oxidation states, we can follow these steps:

### Step 1: Identify the oxidation states
- The oxidation state of X is +2.
- The oxidation state of Y is +5.
- The oxidation state of Z is -2.

### Step 2: Set up the equation for the compound
The overall charge of the compound must equal zero. If we denote the number of atoms of X, Y, and Z in the formula as \( a \), \( b \), and \( c \) respectively, we can express the total charge as follows:

\[ \text{Total charge} = a \cdot (+2) + b \cdot (+5) + c \cdot (-2) = 0 \]

### Step 3: Analyze the possible formulas
We will evaluate the possible formulas provided in the options to see which one satisfies the equation above.

#### Option A: \( XY2Z \)
- Charge = \( (+2) + 2 \cdot (+5) + 1 \cdot (-2) \)
- Charge = \( 2 + 10 - 2 = 10 \) (not equal to 0)

#### Option B: \( Y2X2Z \)
- Charge = \( 2 \cdot (+5) + 2 \cdot (+2) + 1 \cdot (-2) \)
- Charge = \( 10 + 4 - 2 = 12 \) (not equal to 0)

#### Option C: \( X3Y2Z8 \)
- Charge = \( 3 \cdot (+2) + 2 \cdot (+5) + 8 \cdot (-2) \)
- Charge = \( 6 + 10 - 16 = 0 \) (equal to 0)

#### Option D: \( Y3X8Z2 \)
- Charge = \( 3 \cdot (+5) + 8 \cdot (+2) + 2 \cdot (-2) \)
- Charge = \( 15 + 16 - 4 = 27 \) (not equal to 0)

### Conclusion
The only formula that results in a total charge of zero is option C: \( X3Y2Z8 \).

### Final Answer
The possible formula of the compound is \( X3Y2Z8 \).

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