Which of the following shows nitrogen with its increasing order of oxidation number.

Options

A. `N_(2)O lt NO lt NO_(2) lt NO_(3)^(-) lt NH_(4)^(+)`
B. `NH_(4)^(+) lt N_(2)O lt NO lt NO_(2) lt NO_(3)^(-)`
C. `NH_(4)^(+) lt N_(2)O lt NO_(2) lt NO_(3)^(-) lt NO`
D. `NH_(4)^(+) lt NO lt N_(2)O lt NO_(2) lt NO_(3)^(-)`

Explanation

To determine the increasing order of oxidation numbers of nitrogen in the given compounds, we will calculate the oxidation number of nitrogen in each compound step by step.

### Step 1: Calculate the oxidation number for N2O
1. Let the oxidation number of nitrogen be \( X \).
2. The oxidation number of oxygen is \(-2\).
3. The equation for the compound N2O is:
\[ 2X + (-2) = 0 \]
4. Simplifying this gives:
\[ 2X - 2 = 0 \implies 2X = 2 \implies X = +1 \]
Therefore, the oxidation number of nitrogen in N2O is **+1**.

### Step 2: Calculate the oxidation number for NO
1. Let the oxidation number of nitrogen be \( X \).
2. The oxidation number of oxygen is \(-2\).
3. The equation for the compound NO is:
\[ X + (-2) = 0 \]
4. Simplifying this gives:
\[ X - 2 = 0 \implies X = +2 \]
Therefore, the oxidation number of nitrogen in NO is **+2**.

### Step 3: Calculate the oxidation number for NO2
1. Let the oxidation number of nitrogen be \( X \).
2. The oxidation number of oxygen is \(-2\).
3. The equation for the compound NO2 is:
\[ X + 2(-2) = 0 \]
4. Simplifying this gives:
\[ X - 4 = 0 \implies X = +4 \]
Therefore, the oxidation number of nitrogen in NO2 is **+4**.

### Step 4: Calculate the oxidation number for NH4+
1. Let the oxidation number of nitrogen be \( X \).
2. The oxidation number of hydrogen is \( +1 \) and there are 4 hydrogen atoms.
3. The equation for the ion NH4+ is:
\[ X + 4(+1) = +1 \]
4. Simplifying this gives:
\[ X + 4 = 1 \implies X = 1 - 4 \implies X = -3 \]
Therefore, the oxidation number of nitrogen in NH4+ is **-3**.

### Step 5: Calculate the oxidation number for NO3-
1. Let the oxidation number of nitrogen be \( X \).
2. The oxidation number of oxygen is \(-2\) and there are 3 oxygen atoms.
3. The equation for the ion NO3- is:
\[ X + 3(-2) = -1 \]
4. Simplifying this gives:
\[ X - 6 = -1 \implies X = -1 + 6 \implies X = +5 \]
Therefore, the oxidation number of nitrogen in NO3- is **+5**.

### Summary of Oxidation Numbers:
- N2O: +1
- NO: +2
- NO2: +4
- NH4+: -3
- NO3-: +5

### Step 6: Arrange in increasing order
Now, we can arrange the oxidation numbers in increasing order:
- NH4+: -3
- N2O: +1
- NO: +2
- NO2: +4
- NO3-: +5

Thus, the increasing order of oxidation numbers of nitrogen is:
**NH4+ < N2O < NO < NO2 < NO3-**

### Final Answer:
The correct answer is option **2** (if that corresponds to the increasing order derived).