Which has the bond order `1/2`?

Options

A. `O_2`
B. `N_2`
C. `F_2`
D. `H_(2)^(+)`

Explanation

To determine which molecule has a bond order of \( \frac{1}{2} \), we can follow these steps:

### Step 1: Understand Bond Order
Bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]
A bond order of \( \frac{1}{2} \) indicates that there is a weak bond between the atoms.

### Step 2: Identify the Total Number of Electrons
We need to check the total number of electrons in the molecules we are considering. For a bond order of \( \frac{1}{2} \), we can use the shortcut mentioned in the video transcript:
- If the total number of electrons is 9, the bond order is \( \frac{1}{2} \).

### Step 3: Check Common Diatomic Molecules
Let’s consider some common diatomic molecules and their total number of electrons:
- \( \text{H}_2 \) has 2 electrons.
- \( \text{He}_2 \) has 4 electrons.
- \( \text{Li}_2 \) has 6 electrons.
- \( \text{Be}_2 \) has 8 electrons.
- \( \text{B}_2 \) has 10 electrons.
- \( \text{C}_2 \) has 12 electrons.
- \( \text{N}_2 \) has 14 electrons.
- \( \text{O}_2 \) has 16 electrons.
- \( \text{F}_2 \) has 18 electrons.
- \( \text{H}_2^+ \) has 1 electron (which gives a bond order of 1).
- \( \text{H}_2^- \) has 3 electrons (which gives a bond order of 1).

### Step 4: Identify the Molecule with 9 Electrons
From the list, we can see that the molecule that has a total of 9 electrons is \( \text{H}_2^- \) (the hydrogen anion).

### Step 5: Calculate the Bond Order for \( \text{H}_2^- \)
For \( \text{H}_2^- \):
- Bonding electrons = 2 (from the 2 electrons in the bonding molecular orbital)
- Antibonding electrons = 0 (no electrons in the antibonding molecular orbital)

Using the bond order formula:
\[ \text{Bond Order} = \frac{1}{2} \times (2 - 0) = \frac{1}{2} \times 2 = 1 \]
However, since we are looking for \( \frac{1}{2} \), we realize that the bond order for \( \text{H}_2^- \) is actually 1, and we need to consider the \( \text{He}^- \) or other configurations.

### Conclusion
The molecule with a bond order of \( \frac{1}{2} \) is \( \text{He}^- \) (which has 9 electrons).

### Final Answer
The molecule with a bond order of \( \frac{1}{2} \) is \( \text{H}_2^- \).