Oxidation number of potassium in ` K _ 2 O`, ` K_2 O _ 2 and K O _ 2 ` , respectively, is :

Options

A. (a) ` + 1 ,+2 and + 4 `
B. (b) ` + 1, + 1 and +1 `
C. (c) `+1,+4 and +2`
D. (d) ` + 2, + 1 and + ( 1 ) /(2) `

Answer

To find the oxidation number of potassium (K) in the compounds \( K_2O \), \( K_2O_2 \), and \( KO_2 \), we will analyze each compound step by step.

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

1. **Identify the oxidation state of oxygen**: In \( K_2O \), oxygen typically has an oxidation state of \(-2\).
2. **Set up the equation**: Let the oxidation number of potassium be \( x \). Since there are 2 potassium atoms, the equation can be set up as:
\[ 2x + (-2) = 0 \]
3. **Solve for \( x \)**:
\[ 2x - 2 = 0 \\ 2x = 2 \\ x = +1 \]
4. **Conclusion**: The oxidation number of potassium in \( K_2O \) is \( +1 \).

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

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

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

1. **Identify the oxidation state of oxygen**: In \( KO_2 \) (a superoxide), each oxygen has an oxidation state of \(-\frac{1}{2}\).
2. **Set up the equation**: Let the oxidation number of potassium be \( x \). The equation is:
\[ x + 2\left(-\frac{1}{2}\right) = 0 \]
3. **Solve for \( x \)**:
\[ x - 1 = 0 \\ x = +1 \]
4. **Conclusion**: The oxidation number of potassium in \( KO_2 \) is \( +1 \).

### Final Answer

The oxidation numbers of potassium in \( K_2O \), \( K_2O_2 \), and \( KO_2 \) are respectively:
- \( K_2O \): \( +1 \)
- \( K_2O_2 \): \( +1 \)
- \( KO_2 \): \( +1 \)

Thus, the final answer is \( +1, +1, +1 \).