How many of the following oxides of nitrogen are paramangnetic ?
(i) `N_(2)O` (ii) `NO` (iii) `N_(2)O_(3)` (iv) `NO_(2)`
(v) `N_(2)O_(4)` (vi) `N_(2)O_(5)` (vii) `NO_(2)^(o+)` (viii) `NO_(2)^(Theta)`
(ix) `NO_(3)^(Theta)` .

Answer

To determine how many of the given oxides of nitrogen are paramagnetic, we need to check for unpaired electrons in each oxide. A compound is paramagnetic if it has unpaired electrons and diamagnetic if all electrons are paired.

### Step-by-Step Solution:

1. **Identify the Oxides and Their Valence Electrons:**
- (i) **N₂O**:
- Nitrogen (N) has 5 valence electrons, and there are 2 nitrogen atoms: \(2 \times 5 = 10\).
- Oxygen (O) has 6 valence electrons: \(1 \times 6 = 6\).
- Total = \(10 + 6 = 16\) (even, not paramagnetic).

- (ii) **NO**:
- Nitrogen (N) has 5 valence electrons: \(1 \times 5 = 5\).
- Oxygen (O) has 6 valence electrons: \(1 \times 6 = 6\).
- Total = \(5 + 6 = 11\) (odd, paramagnetic).

- (iii) **N₂O₃**:
- Nitrogen (N) has 5 valence electrons, and there are 2 nitrogen atoms: \(2 \times 5 = 10\).
- Oxygen (O) has 6 valence electrons, and there are 3 oxygen atoms: \(3 \times 6 = 18\).
- Total = \(10 + 18 = 28\) (even, not paramagnetic).

- (iv) **NO₂**:
- Nitrogen (N) has 5 valence electrons: \(1 \times 5 = 5\).
- Oxygen (O) has 6 valence electrons, and there are 2 oxygen atoms: \(2 \times 6 = 12\).
- Total = \(5 + 12 = 17\) (odd, paramagnetic).

- (v) **N₂O₄**:
- Nitrogen (N) has 5 valence electrons, and there are 2 nitrogen atoms: \(2 \times 5 = 10\).
- Oxygen (O) has 6 valence electrons, and there are 4 oxygen atoms: \(4 \times 6 = 24\).
- Total = \(10 + 24 = 34\) (even, not paramagnetic).

- (vi) **N₂O₅**:
- Nitrogen (N) has 5 valence electrons, and there are 2 nitrogen atoms: \(2 \times 5 = 10\).
- Oxygen (O) has 6 valence electrons, and there are 5 oxygen atoms: \(5 \times 6 = 30\).
- Total = \(10 + 30 = 40\) (even, not paramagnetic).

- (vii) **NO₂⁺**:
- Nitrogen (N) has 5 valence electrons: \(1 \times 5 = 5\).
- Oxygen (O) has 6 valence electrons, and there are 2 oxygen atoms: \(2 \times 6 = 12\).
- Positive charge means we subtract 1 electron: \(5 + 12 - 1 = 16\) (even, not paramagnetic).

- (viii) **NO₂⁻**:
- Nitrogen (N) has 5 valence electrons: \(1 \times 5 = 5\).
- Oxygen (O) has 6 valence electrons, and there are 2 oxygen atoms: \(2 \times 6 = 12\).
- Negative charge means we add 1 electron: \(5 + 12 + 1 = 18\) (even, not paramagnetic).

- (ix) **NO₃⁻**:
- Nitrogen (N) has 5 valence electrons: \(1 \times 5 = 5\).
- Oxygen (O) has 6 valence electrons, and there are 3 oxygen atoms: \(3 \times 6 = 18\).
- Negative charge means we add 1 electron: \(5 + 18 + 1 = 24\) (even, not paramagnetic).

2. **Count the Paramagnetic Oxides:**
- From the analysis, the paramagnetic oxides are:
- (ii) NO
- (iv) NO₂

Thus, there are **2 paramagnetic oxides** among the given options.

### Final Answer:
**2**