The correct decreasing order ofoxidation number ofoxygen in compounds `BaO_2`, `O_3`, `KO_2` and `OF_2` is :

Options

A. `BaO_2 gt KO_2 gt O_3 gt OF_2`
B. `OF_2 gt O_3 gt KO_2 gt BaO_2`
C. `KO_2 gt OF_2 gt O_3 gt BaO_2`
D. `BaO_2 gt O_3 gt OF_2 gt KO_2`

Explanation

To determine the correct decreasing order of the oxidation number of oxygen in the compounds \( \text{BaO}_2 \), \( \text{O}_3 \), \( \text{KO}_2 \), and \( \text{OF}_2 \), we will calculate the oxidation state of oxygen in each compound step by step.

### Step 1: Calculate the oxidation state of oxygen in \( \text{BaO}_2 \)

1. The oxidation state of barium (Ba) is +2 (as it is in Group 2).
2. Let the oxidation state of oxygen be \( x \).
3. The formula for the compound is neutral, so:
\[ +2 + 2x = 0 \]
4. Solving for \( x \):
\[ 2x = -2 \implies x = -1 \]
Thus, the oxidation state of oxygen in \( \text{BaO}_2 \) is -1.

### Step 2: Calculate the oxidation state of oxygen in \( \text{O}_3 \)

1. In ozone (\( \text{O}_3 \)), all three oxygen atoms are the same.
2. Let the oxidation state of oxygen be \( x \).
3. The total oxidation state must equal 0:
\[ 3x = 0 \]
4. Solving for \( x \):
\[ x = 0 \]
Thus, the oxidation state of oxygen in \( \text{O}_3 \) is 0.

### Step 3: Calculate the oxidation state of oxygen in \( \text{KO}_2 \)

1. The oxidation state of potassium (K) is +1 (as it is in Group 1).
2. Let the oxidation state of oxygen be \( x \).
3. The formula for the compound is neutral, so:
\[ +1 + 2x = 0 \]
4. Solving for \( x \):
\[ 2x = -1 \implies x = -\frac{1}{2} \]
Thus, the oxidation state of oxygen in \( \text{KO}_2 \) is -1/2.

### Step 4: Calculate the oxidation state of oxygen in \( \text{OF}_2 \)

1. The oxidation state of fluorine (F) is -1 (as it is more electronegative than oxygen).
2. Let the oxidation state of oxygen be \( x \).
3. The formula for the compound is neutral, so:
\[ x + 2(-1) = 0 \]
4. Solving for \( x \):
\[ x - 2 = 0 \implies x = +2 \]
Thus, the oxidation state of oxygen in \( \text{OF}_2 \) is +2.

### Step 5: Arrange the oxidation states in decreasing order

Now we have the oxidation states of oxygen in each compound:
- \( \text{OF}_2 \): +2
- \( \text{O}_3 \): 0
- \( \text{KO}_2 \): -1/2
- \( \text{BaO}_2 \): -1

The correct decreasing order of oxidation numbers of oxygen is:
\[ \text{OF}_2 > \text{O}_3 > \text{KO}_2 > \text{BaO}_2 \]

### Final Answer:
The correct decreasing order of oxidation number of oxygen in the compounds \( \text{BaO}_2 \), \( \text{O}_3 \), \( \text{KO}_2 \), and \( \text{OF}_2 \) is:
\[ \text{OF}_2 > \text{O}_3 > \text{KO}_2 > \text{BaO}_2 \]