The correct order of the oxidation states of nitrogen in `NO, N_(2)O, NO_(2)` and `N_(2)O_(3)` is :

Options

A. `NO_(2) lt NO lt N_(2)O_(3) lt N_(2)O`
B. `N_(2)O lt N_(2)O_(3) lt NO lt NO_(2)`
C. `N_(2)O lt NO lt N_(2)O_(3) lt NO_(2)`
D. `NO_(2) lt N_(2)O_(3) lt NO lt N_(2)O`

Explanation

To determine the correct order of the oxidation states of nitrogen in the compounds NO, N₂O, NO₂, and N₂O₃, we will calculate the oxidation state of nitrogen in each compound step by step.

### Step 1: Calculate the oxidation state of nitrogen in NO
1. In the compound NO, let the oxidation state of nitrogen be \( x \).
2. The oxidation state of oxygen is typically \(-2\).
3. Since the compound is neutral, the sum of the oxidation states must equal 0:
\[ x + (-2) = 0 \]
4. Solving for \( x \):
\[ x - 2 = 0 \implies x = +2 \]

### Step 2: Calculate the oxidation state of nitrogen in N₂O
1. In the compound N₂O, let the oxidation state of nitrogen be \( x \).
2. There are 2 nitrogen atoms, so the total contribution from nitrogen is \( 2x \).
3. The oxidation state of oxygen is \(-2\).
4. The sum of the oxidation states must equal 0:
\[ 2x + (-2) = 0 \]
5. Solving for \( x \):
\[ 2x - 2 = 0 \implies 2x = 2 \implies x = +1 \]

### Step 3: Calculate the oxidation state of nitrogen in NO₂
1. In the compound NO₂, let the oxidation state of nitrogen be \( x \).
2. The total contribution from nitrogen is \( x \) and from the two oxygen atoms is \( 2 \times (-2) = -4 \).
3. The sum of the oxidation states must equal 0:
\[ x + (-4) = 0 \]
4. Solving for \( x \):
\[ x - 4 = 0 \implies x = +4 \]

### Step 4: Calculate the oxidation state of nitrogen in N₂O₃
1. In the compound N₂O₃, let the oxidation state of nitrogen be \( x \).
2. There are 2 nitrogen atoms, so the total contribution from nitrogen is \( 2x \).
3. The contribution from the three oxygen atoms is \( 3 \times (-2) = -6 \).
4. The sum of the oxidation states must equal 0:
\[ 2x + (-6) = 0 \]
5. Solving for \( x \):
\[ 2x - 6 = 0 \implies 2x = 6 \implies x = +3 \]

### Summary of Oxidation States
- NO: +2
- N₂O: +1
- NO₂: +4
- N₂O₃: +3

### Step 5: Arrange the oxidation states in order
Now we can arrange the oxidation states from lowest to highest:
1. N₂O: +1
2. NO: +2
3. N₂O₃: +3
4. NO₂: +4

### Final Answer
The correct order of the oxidation states of nitrogen in the compounds NO, N₂O, NO₂, and N₂O₃ is:
**N₂O < NO < N₂O₃ < NO₂**