Which of the following statements is`//`are correct?

Options

A. The oxidation states of `N` in `NH_(3), HN_(3)`, and `N_(2)H_(4)` are `-3, -1//3`, and `-2`, respectively.
B. The oxidation state of `N` in `NO_(2), N_(2)O_(4), and `NO_(2)^(-)` are `+4, +4`, and `+3`, respectively.
C. The oxidation states of `N` in `NH_(2)OH, NO`, and `HNO_(3)` are `-1, +2`, and ` +5`, respectively.
D. The oxidation states of `N` in `N_(2)O` and `HCN` are `+1` and `-3`, respectively.

Explanation

To determine which statements regarding the oxidation states of nitrogen in various compounds are correct, we will analyze each compound one by one, calculating the oxidation state of nitrogen (N) in each case.

### Step-by-Step Solution:

1. **Determine the oxidation state of nitrogen in NH3 (Ammonia)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for ammonia is \( NH_3 \).
- The total charge of the molecule is 0 (since it is neutral).
- The oxidation state of hydrogen (H) is +1.
- Therefore, the equation becomes:
\[ x + 3(+1) = 0 \]
\[ x + 3 = 0 \implies x = -3 \]
- **Oxidation state of nitrogen in NH3 is -3**.

2. **Determine the oxidation state of nitrogen in HN3 (Hydrazoic acid)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for hydrazoic acid is \( HN_3 \).
- The total charge of the molecule is 0.
- The oxidation state of hydrogen is +1.
- Therefore, the equation becomes:
\[ +1 + 3x = 0 \]
\[ 3x = -1 \implies x = -\frac{1}{3} \]
- **Oxidation state of nitrogen in HN3 is -1/3**.

3. **Determine the oxidation state of nitrogen in N2H4 (Hydrazine)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for hydrazine is \( N_2H_4 \).
- The total charge of the molecule is 0.
- The oxidation state of hydrogen is +1.
- Therefore, the equation becomes:
\[ 2x + 4(+1) = 0 \]
\[ 2x + 4 = 0 \implies 2x = -4 \implies x = -2 \]
- **Oxidation state of nitrogen in N2H4 is -2**.

4. **Determine the oxidation state of nitrogen in NO2 (Nitrogen Dioxide)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for nitrogen dioxide is \( NO_2 \).
- The total charge of the molecule is 0.
- The oxidation state of oxygen is -2.
- Therefore, the equation becomes:
\[ x + 2(-2) = 0 \]
\[ x - 4 = 0 \implies x = +4 \]
- **Oxidation state of nitrogen in NO2 is +4**.

5. **Determine the oxidation state of nitrogen in N2O4 (Dinitrogen Tetroxide)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for dinitrogen tetroxide is \( N_2O_4 \).
- The total charge of the molecule is 0.
- The oxidation state of oxygen is -2.
- Therefore, the equation becomes:
\[ 2x + 4(-2) = 0 \]
\[ 2x - 8 = 0 \implies 2x = 8 \implies x = +4 \]
- **Oxidation state of nitrogen in N2O4 is +4**.

6. **Determine the oxidation state of nitrogen in NO2- (Nitrite Ion)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for the nitrite ion is \( NO_2^- \).
- The total charge of the ion is -1.
- The oxidation state of oxygen is -2.
- Therefore, the equation becomes:
\[ x + 2(-2) = -1 \]
\[ x - 4 = -1 \implies x = +3 \]
- **Oxidation state of nitrogen in NO2- is +3**.

7. **Determine the oxidation state of nitrogen in NH2OH (Hydroxylamine)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for hydroxylamine is \( NH_2OH \).
- The total charge of the molecule is 0.
- The oxidation state of hydrogen is +1 and oxygen is -2.
- Therefore, the equation becomes:
\[ x + 2(+1) + (-2) = 0 \]
\[ x + 2 - 2 = 0 \implies x = 0 \]
- **Oxidation state of nitrogen in NH2OH is 0**.

8. **Determine the oxidation state of nitrogen in NO (Nitric Oxide)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for nitric oxide is \( NO \).
- The total charge of the molecule is 0.
- The oxidation state of oxygen is -2.
- Therefore, the equation becomes:
\[ x + (-2) = 0 \]
\[ x = +2 \]
- **Oxidation state of nitrogen in NO is +2**.

9. **Determine the oxidation state of nitrogen in HNO3 (Nitric Acid)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for nitric acid is \( HNO_3 \).
- The total charge of the molecule is 0.
- The oxidation state of hydrogen is +1 and oxygen is -2.
- Therefore, the equation becomes:
\[ +1 + x + 3(-2) = 0 \]
\[ +1 + x - 6 = 0 \implies x - 5 = 0 \implies x = +5 \]
- **Oxidation state of nitrogen in HNO3 is +5**.

10. **Determine the oxidation state of nitrogen in N2O (Dinitrogen Monoxide)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for dinitrogen monoxide is \( N_2O \).
- The total charge of the molecule is 0.
- The oxidation state of oxygen is -2.
- Therefore, the equation becomes:
\[ 2x + (-2) = 0 \]
\[ 2x - 2 = 0 \implies 2x = 2 \implies x = +1 \]
- **Oxidation state of nitrogen in N2O is +1**.

11. **Determine the oxidation state of nitrogen in HCN (Hydrogen Cyanide)**:
- Let the oxidation state of nitrogen be \( x \).
- The formula for hydrogen cyanide is \( HCN \).
- The total charge of the molecule is 0.
- The oxidation state of hydrogen is +1 and carbon is +4.
- Therefore, the equation becomes:
\[ +1 + x + 4 = 0 \]
\[ x + 5 = 0 \implies x = -5 \]
- **Oxidation state of nitrogen in HCN is -5**.

### Conclusion:
Now we can summarize the oxidation states calculated:
- NH3: -3
- HN3: -1/3
- N2H4: -2
- NO2: +4
- N2O4: +4
- NO2-: +3
- NH2OH: 0
- NO: +2
- HNO3: +5
- N2O: +1
- HCN: -5