How many bonds `B_2` have ?

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine how many bonds the B2 molecule has, we can follow these steps:

### Step 1: Determine the total number of electrons in B2
- Each boron (B) atom has 5 electrons. Since B2 consists of two boron atoms, the total number of electrons is:
\[ \text{Total electrons} = 2 \times 5 = 10 \text{ electrons} \]

### Step 2: Write the molecular electronic configuration of B2
- The molecular electronic configuration for B2 can be written as follows:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p_x}^1 \pi_{2p_y}^1 \sigma_{2p_z}^0 \]
- Here, the bonding molecular orbitals (BMOs) are filled first, followed by the antibonding molecular orbitals (AMOs).

### Step 3: Count the electrons in bonding and antibonding molecular orbitals
- **Bonding Molecular Orbitals (BMOs)**:
- From the configuration, the electrons in BMOs are:
- \( \sigma_{1s}^2 \) (2 electrons)
- \( \sigma_{2s}^2 \) (2 electrons)
- \( \pi_{2p_x}^1 \) (1 electron)
- \( \pi_{2p_y}^1 \) (1 electron)
- Total in BMOs = \( 2 + 2 + 1 + 1 = 6 \) electrons

- **Antibonding Molecular Orbitals (AMOs)**:
- From the configuration, the electrons in AMOs are:
- \( \sigma^*_{1s}^2 \) (2 electrons)
- \( \sigma^*_{2s}^2 \) (2 electrons)
- Total in AMOs = \( 2 + 2 = 4 \) electrons

### Step 4: Calculate the bond order
- The bond order is calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \left( \text{Number of electrons in BMOs} - \text{Number of electrons in AMOs} \right) \]
- Plugging in the numbers:
\[ \text{Bond Order} = \frac{1}{2} \left( 6 - 4 \right) = \frac{1}{2} \times 2 = 1 \]

### Step 5: Conclusion
- The bond order of B2 is 1, which indicates that there is one bond present between the two boron atoms.

### Final Answer:
- The B2 molecule has **1 bond**.

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