The calculated bond order in `H_(2)^(+)` ion is

Options

A. 0
B. `1/2`
C. `-(1)/(2)`
D. `1`

Explanation

To calculate the bond order of the \( H_2^+ \) ion, we can follow these steps:

### Step 1: Understand the Molecular Orbital Theory (MOT) for Hydrogen
- The molecular orbital configuration for two hydrogen atoms (H) involves the combination of their 1s atomic orbitals. When two hydrogen atoms come together, they form two molecular orbitals: one bonding molecular orbital (\( \sigma_{1s} \)) and one antibonding molecular orbital (\( \sigma^*_{1s} \)).

### Step 2: Write the Electron Configuration
- For the \( H_2^+ \) ion, we have two hydrogen atoms, but one electron is removed due to the positive charge.
- The electron configuration for \( H_2 \) would be \( \sigma_{1s}^2 \) (both electrons in the bonding orbital). For \( H_2^+ \), we remove one electron, resulting in the configuration \( \sigma_{1s}^1 \).

### Step 3: Identify the Number of Electrons in Each Orbital
- In \( H_2^+ \):
- Bonding molecular orbital (\( \sigma_{1s} \)): 1 electron
- Antibonding molecular orbital (\( \sigma^*_{1s} \)): 0 electrons

### Step 4: Use the Bond Order Formula
- The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} \left( N_b - N_a \right) \]
where \( N_b \) is the number of electrons in bonding orbitals and \( N_a \) is the number of electrons in antibonding orbitals.

### Step 5: Substitute the Values
- Substitute \( N_b = 1 \) and \( N_a = 0 \) into the formula:
\[ \text{Bond Order} = \frac{1}{2} \left( 1 - 0 \right) = \frac{1}{2} \]

### Step 6: Conclusion
- The bond order of the \( H_2^+ \) ion is \( 0.5 \).

### Final Answer
The calculated bond order in \( H_2^+ \) ion is \( 0.5 \).

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