Which of the following facts given is not correct?
(I) Bond length order, `H_(2)^(-)-H_(2)^(+)gtH_(2)`
(II) `O_(2)^(+), NO, N_(2)^(-)` have same bond order of `2(1)/(2)`
(II) Bond order can assume any value including zero upto four
(IV) `NO_(3)^(-) and BO_(3)^(-)` have same order for `X-O` bond (where X is central atom)

Options

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

Answer

To solve the question, we need to analyze each of the statements provided and determine which one is incorrect.

### Step-by-Step Solution:

1. **Statement I: Bond length order, H2^(-) > H2^(+) > H2**
- **Analysis**:
- H2 has the highest bond order (1), hence it has the shortest bond length.
- H2^(-) has a bond order of 0.5, and H2^(+) also has a bond order of 0.5.
- Therefore, the bond length order should be H2 < H2^(-) = H2^(+).
- Thus, this statement is **incorrect** because it suggests the opposite order.

2. **Statement II: O2^(+), NO, N2^(-) have the same bond order of 2.5**
- **Analysis**:
- O2^(+) has 15 electrons, which gives it a bond order of 2.5.
- NO has 15 electrons as well, giving it a bond order of 2.5.
- N2^(-) has 15 electrons, resulting in a bond order of 2.5.
- Therefore, this statement is **correct**.

3. **Statement III: Bond order can assume any value including zero up to four**
- **Analysis**:
- Bond order can range from 0 (no bond) to a maximum of 3 (for triple bonds).
- It cannot reach 4; hence, this statement is **incorrect**.

4. **Statement IV: NO3^(-) and BO3^(-) have the same order for X-O bond**
- **Analysis**:
- Both NO3^(-) and BO3^(-) have resonance structures that can be analyzed.
- The bond order for the X-O bond in both cases is indeed the same due to resonance.
- Therefore, this statement is **correct**.

### Conclusion:
The statements that are incorrect are **I** and **III**. However, since the question asks for which fact is not correct, we can conclude that the most clearly incorrect statement is **III**.

### Final Answer:
The statement that is not correct is **III**: "Bond order can assume any value including zero up to four."