Match the following and choose the correct option given below
(a) `N_(2)toN_(2)^(+)` (p) bond order increases
(b) `N_(2)toN_(2)^(-)` (q) bond order decreases
( c) `O_(2)toO_(2)^(+)` ( r) paramagnetism decreases
(d) `O_(2)toO_(2)^(-)` (s) paramagnetism desreases
(t) No change in bond order

Options

A. `{:(a,b,c,d),(s,p,r,q):}`
B. `{:(a,b,c,d),(s,p,q,r):}`
C. `{:(a,b,c,d),(r,q,s,p):}`
D. `{:(a,b,c,d),(p,s,q,r):}`

Explanation

To solve the question, we need to analyze the bond order and paramagnetism of the given molecular species based on their molecular orbital configurations. Let's break down the steps:

### Step 1: Determine the bond order and paramagnetism for \(N_2\) to \(N_2^+\)
- **Molecular Orbital Configuration of \(N_2\)**:
- \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \pi 2p_x^2 = \pi 2p_y^2 \sigma 2p_z^2 \)
- Total Electrons = 14 (2 in each of the 7 orbitals)
- Bonding Electrons = 10, Anti-bonding Electrons = 4
- **Bond Order**: \( \frac{10 - 4}{2} = 3 \)
- **Paramagnetism**: Diamagnetic (no unpaired electrons)

- **Molecular Orbital Configuration of \(N_2^+\)**:
- Total Electrons = 13 (1 electron removed)
- Configuration: \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \pi 2p_x^2 = \pi 2p_y^2 \sigma 2p_z^1 \)
- Bonding Electrons = 9, Anti-bonding Electrons = 4
- **Bond Order**: \( \frac{9 - 4}{2} = 2.5 \)
- **Paramagnetism**: Paramagnetic (1 unpaired electron)

### Step 2: Determine the bond order and paramagnetism for \(N_2\) to \(N_2^-\)
- **Molecular Orbital Configuration of \(N_2^-\)**:
- Total Electrons = 15 (1 electron added)
- Configuration: \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \pi 2p_x^2 = \pi 2p_y^2 \sigma 2p_z^2 \pi^* 2p_x^1 \)
- Bonding Electrons = 10, Anti-bonding Electrons = 5
- **Bond Order**: \( \frac{10 - 5}{2} = 2.5 \)
- **Paramagnetism**: Paramagnetic (1 unpaired electron)

### Step 3: Determine the bond order and paramagnetism for \(O_2\) to \(O_2^+\)
- **Molecular Orbital Configuration of \(O_2\)**:
- Total Electrons = 16
- Configuration: \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 = \pi 2p_y^2 \pi^* 2p_x^1 = \pi^* 2p_y^1 \)
- Bonding Electrons = 10, Anti-bonding Electrons = 6
- **Bond Order**: \( \frac{10 - 6}{2} = 2 \)
- **Paramagnetism**: Paramagnetic (2 unpaired electrons)

- **Molecular Orbital Configuration of \(O_2^+\)**:
- Total Electrons = 15 (1 electron removed)
- Configuration: \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 = \pi 2p_y^1 \)
- Bonding Electrons = 10, Anti-bonding Electrons = 5
- **Bond Order**: \( \frac{10 - 5}{2} = 2.5 \)
- **Paramagnetism**: Paramagnetic (1 unpaired electron)

### Step 4: Determine the bond order and paramagnetism for \(O_2\) to \(O_2^-\)
- **Molecular Orbital Configuration of \(O_2^-\)**:
- Total Electrons = 17 (1 electron added)
- Configuration: \( \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 = \pi 2p_y^2 \pi^* 2p_x^2 \)
- Bonding Electrons = 10, Anti-bonding Electrons = 7
- **Bond Order**: \( \frac{10 - 7}{2} = 1.5 \)
- **Paramagnetism**: Paramagnetic (2 unpaired electrons)

### Step 5: Match the results
- (a) \(N_2\) to \(N_2^+\) → Bond order decreases (Q), paramagnetism increases (R)
- (b) \(N_2\) to \(N_2^-\) → Bond order decreases (Q), paramagnetism increases (R)
- (c) \(O_2\) to \(O_2^+\) → Bond order increases (P), paramagnetism decreases (S)
- (d) \(O_2\) to \(O_2^-\) → Bond order decreases (Q), paramagnetism decreases (S)

### Final Matching
- (a) → (Q, R)
- (b) → (Q, R)
- (c) → (P, S)
- (d) → (Q, S)

### Correct Option
The correct option based on the matches is option 3.