Consider the statements :
I . Bond length in `N_(2)^(+) is 0.002 Å` greater than in `N_(2)`
II. Bond length in `NO^(+) is 0.09 Å` less than in NO
III. `O_(2)^(2-)` has shorter bond length than `O_(2)`
which of the following statements are ture ?

Options

A. I and II
B. II and III
C. I, II and III
D. I and III

Explanation

To determine the truth of the statements regarding bond lengths and bond orders in the given molecules, we will analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** Bond length in \(N_2^+\) is 0.002 Å greater than in \(N_2\).

- **Bond Order Calculation:**
- For \(N_2\):
- Total electrons = 14 (7 from each nitrogen).
- Bond order = \( \frac{(10 - 4)}{2} = 3 \) (10 bonding electrons and 4 antibonding electrons).
- For \(N_2^+\):
- Total electrons = 13 (one electron removed).
- Bond order = \( \frac{(10 - 3)}{2} = 2.5 \).

- **Conclusion for Statement I:**
- Since \(N_2^+\) has a lower bond order than \(N_2\), the bond length in \(N_2^+\) will be greater than in \(N_2\). Thus, this statement is **true**.

### Step 2: Analyze Statement II
**Statement II:** Bond length in \(NO^+\) is 0.09 Å less than in \(NO\).

- **Bond Order Calculation:**
- For \(NO\):
- Total electrons = 15 (7 from nitrogen and 8 from oxygen).
- Bond order = \( \frac{(10 - 5)}{2} = 2.5 \).
- For \(NO^+\):
- Total electrons = 14 (one electron removed).
- Bond order = \( \frac{(10 - 4)}{2} = 3 \).

- **Conclusion for Statement II:**
- Since \(NO^+\) has a higher bond order than \(NO\), the bond length in \(NO^+\) will be less than in \(NO\). Thus, this statement is **true**.

### Step 3: Analyze Statement III
**Statement III:** \(O_2^{2-}\) has shorter bond length than \(O_2\).

- **Bond Order Calculation:**
- For \(O_2\):
- Total electrons = 16 (8 from each oxygen).
- Bond order = \( \frac{(10 - 6)}{2} = 2 \).
- For \(O_2^{2-}\):
- Total electrons = 18 (two electrons added).
- Bond order = \( \frac{(10 - 8)}{2} = 1 \).

- **Conclusion for Statement III:**
- Since \(O_2^{2-}\) has a lower bond order than \(O_2\), the bond length in \(O_2^{2-}\) will be greater than in \(O_2\). Thus, this statement is **false**.

### Final Conclusion
The true statements are:
- Statement I: True
- Statement II: True
- Statement III: False

Therefore, the correct answer is that **Statements I and II are true**.