Oxidation number of oxygen in `K_2O,K_2O_2` and `KO_2` respectively is :

Options

A. -2,-2,-2
B. -2,-1,-2
C. `-1,-2,-1/2`
D. `-2,-1,-1/2`

Explanation

To determine the oxidation number of oxygen in the compounds \( K_2O \), \( K_2O_2 \), and \( KO_2 \), we will follow these steps:

### Step 1: Determine the oxidation number of oxygen in \( K_2O \)

1. **Identify the oxidation state of potassium (K)**: Potassium (K) has an oxidation state of +1.
2. **Set up the equation**: For \( K_2O \):
\[ 2(+1) + x = 0 \]
where \( x \) is the oxidation state of oxygen.
3. **Solve for \( x \)**:
\[ 2 + x = 0 \implies x = -2 \]
4. **Conclusion**: The oxidation number of oxygen in \( K_2O \) is **-2**.

### Step 2: Determine the oxidation number of oxygen in \( K_2O_2 \)

1. **Identify the oxidation state of potassium (K)**: Again, K has an oxidation state of +1.
2. **Set up the equation**: For \( K_2O_2 \):
\[ 2(+1) + 2x = 0 \]
3. **Solve for \( x \)**:
\[ 2 + 2x = 0 \implies 2x = -2 \implies x = -1 \]
4. **Conclusion**: The oxidation number of oxygen in \( K_2O_2 \) is **-1**.

### Step 3: Determine the oxidation number of oxygen in \( KO_2 \)

1. **Identify the oxidation state of potassium (K)**: K has an oxidation state of +1.
2. **Set up the equation**: For \( KO_2 \):
\[ +1 + 2x = 0 \]
3. **Solve for \( x \)**:
\[ 1 + 2x = 0 \implies 2x = -1 \implies x = -\frac{1}{2} \]
4. **Conclusion**: The oxidation number of oxygen in \( KO_2 \) is **-1/2**.

### Final Answer

The oxidation numbers of oxygen in \( K_2O \), \( K_2O_2 \), and \( KO_2 \) are **-2, -1, and -1/2**, respectively.

### Summary of Results
- \( K_2O \): -2
- \( K_2O_2 \): -1
- \( KO_2 \): -1/2