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

Options

A. `ABC_(3)`
B. `B_(2)(AC_(3))_(2)`
C. `A_(3)(BC_(4))_(2)`
D. `A_(3)(BC_(3))_(2)`

Explanation

To find the possible formula of the compound containing atoms A, B, and C with given oxidation states, we will follow these steps:

### Step 1: Understand the oxidation states
- The oxidation number of A is +2.
- The oxidation number of B is +5.
- The oxidation number of C is -2.

### Step 2: Use the rule that the sum of oxidation states in a neutral compound is zero
For a compound to be neutral, the sum of the oxidation states of all the atoms must equal zero.

### Step 3: Set up the equation
Let the number of atoms of A be \( x \), the number of atoms of B be \( y \), and the number of atoms of C be \( z \). The equation based on oxidation states will be:
\[ 2x + 5y - 2z = 0 \]

### Step 4: Analyze the options given
We will check each option to see if it satisfies the equation \( 2x + 5y - 2z = 0 \).

#### Option A: \( A^1B^1C^3 \)
- \( x = 1, y = 1, z = 3 \)
- Substitute into the equation:
\[ 2(1) + 5(1) - 2(3) = 2 + 5 - 6 = 1 \] (not equal to 0)

#### Option B: \( A^2B^3C^3 \)
- \( x = 2, y = 3, z = 3 \)
- Substitute into the equation:
\[ 2(2) + 5(3) - 2(3) = 4 + 15 - 6 = 13 \] (not equal to 0)

#### Option C: \( A^3B^2C^2 \)
- \( x = 3, y = 2, z = 2 \)
- Substitute into the equation:
\[ 2(3) + 5(2) - 2(2) = 6 + 10 - 4 = 12 \] (not equal to 0)

#### Option D: \( A^2B^1C^3 \)
- \( x = 2, y = 1, z = 3 \)
- Substitute into the equation:
\[ 2(2) + 5(1) - 2(3) = 4 + 5 - 6 = 3 \] (not equal to 0)

### Step 5: Find the correct combination
After checking all options, we find that none of the provided options satisfy the condition of the oxidation states summing to zero.

### Conclusion
The possible formula of the compound cannot be determined from the given options as none satisfy the equation \( 2x + 5y - 2z = 0 \).