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Do H(2)^(+) and H(2)^(-) ions have same ...

Do `H_(2)^(+)` and `H_(2)^(-)` ions have same or different bond orders ?

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To determine whether the ions \( H_2^+ \) and \( H_2^- \) have the same or different bond orders, we will follow these steps: ### Step 1: Determine the Electronic Configuration of \( H_2^+ \) 1. **Identify the number of electrons**: The \( H_2^+ \) ion has one less electron than the neutral \( H_2 \) molecule. The neutral \( H_2 \) has 2 electrons, so \( H_2^+ \) has 1 electron. 2. **Write the electronic configuration**: The electronic configuration for \( H_2^+ \) is \( \sigma_{1s}^1 \). ### Step 2: Calculate the Bond Order for \( H_2^+ \) 1. **Use the bond order formula**: \[ \text{Bond Order} = \frac{1}{2} \left( \text{Number of bonding electrons} - \text{Number of anti-bonding electrons} \right) \] 2. **Substitute the values**: - Number of bonding electrons = 1 (from \( \sigma_{1s}^1 \)) - Number of anti-bonding electrons = 0 (since there are no electrons in \( \sigma_{1s}^* \)) \[ \text{Bond Order} = \frac{1}{2} (1 - 0) = 0.5 \] ### Step 3: Determine the Electronic Configuration of \( H_2^- \) 1. **Identify the number of electrons**: The \( H_2^- \) ion has one more electron than the neutral \( H_2 \) molecule, giving it 3 electrons. 2. **Write the electronic configuration**: The electronic configuration for \( H_2^- \) is \( \sigma_{1s}^2 \sigma_{1s}^*^1 \). ### Step 4: Calculate the Bond Order for \( H_2^- \) 1. **Use the bond order formula**: \[ \text{Bond Order} = \frac{1}{2} \left( \text{Number of bonding electrons} - \text{Number of anti-bonding electrons} \right) \] 2. **Substitute the values**: - Number of bonding electrons = 2 (from \( \sigma_{1s}^2 \)) - Number of anti-bonding electrons = 1 (from \( \sigma_{1s}^*^1 \)) \[ \text{Bond Order} = \frac{1}{2} (2 - 1) = \frac{1}{2} (1) = 0.5 \] ### Conclusion Both \( H_2^+ \) and \( H_2^- \) have the same bond order of 0.5. ### Final Answer **The bond orders of \( H_2^+ \) and \( H_2^- \) are the same, both equal to 0.5.** ---
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