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According to molecular orbital theory,...

According to molecular orbital theory,

A

`C_(2)^(2-)` is expected to be diamagnetic

B

`O_(2)^(2+)` is expected to have a longer bond length than `O_(2)`

C

`N_(2)^(+) and N_(2)^(-)` have the same bond order

D

`He_(2)^(+)` has the same energy as two isolated He atom.

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**Step-by-Step Solution:** 1. **Understanding Molecular Orbital Theory:** - Molecular Orbital (MO) theory explains how atomic orbitals combine to form molecular orbitals, which can be occupied by electrons. The key concepts include bonding and antibonding orbitals, bond order, and magnetic properties of molecules. 2. **Analyzing the Options:** - We have several statements to evaluate based on MO theory. We will analyze each statement one by one. 3. **Statement 1: C2- is diamagnetic.** - C2 has 12 electrons, and C2- has 14 electrons. The electron configuration for C2- is: - σ1s² σ*1s² σ2s² σ*2s² π2p_x² π2p_y² σ2p_z² - All electrons are paired in C2-, confirming that it is diamagnetic. - **Conclusion:** This statement is correct. 4. **Statement 2: O2+ has a longer bond length than O2.** - O2 has 16 electrons, while O2+ has 15 electrons. The bond order for O2 is calculated as: - Bond Order = 1/2 (Number of bonding electrons - Number of antibonding electrons) - For O2: Bonding = 10, Antibonding = 6 → Bond Order = (10 - 6)/2 = 2. - For O2+, the configuration is: - σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x - Bonding = 9, Antibonding = 6 → Bond Order = (9 - 6)/2 = 1.5. - Since a higher bond order indicates a shorter bond length, O2+ has a shorter bond length than O2. - **Conclusion:** This statement is incorrect. 5. **Statement 3: N2+ and N2- have the same bond order.** - N2 has 14 electrons, N2+ has 13 electrons, and N2- has 15 electrons. - For N2: Bond Order = (10 - 4)/2 = 3. - For N2+: Bonding = 9, Antibonding = 4 → Bond Order = (9 - 4)/2 = 2.5. - For N2-: Bonding = 10, Antibonding = 4 → Bond Order = (10 - 4)/2 = 3. - N2+ has a bond order of 2.5, while N2- has a bond order of 3. - **Conclusion:** This statement is incorrect. 6. **Statement 4: Helium 2+ has the same energy as two isolated Helium atoms.** - Helium has 2 electrons, so Helium 2 has 4 electrons, and Helium 2+ has 3 electrons. - The bond order for Helium 2+ is: - Bonding = 2, Antibonding = 1 → Bond Order = (2 - 1)/2 = 0.5. - Isolated Helium atoms do not have a bond order, indicating no bond formation. Therefore, Helium 2+ is more stable (lower energy) than two isolated Helium atoms. - **Conclusion:** This statement is incorrect. 7. **Final Answer:** - The correct statements according to molecular orbital theory are: - Statement 1 is correct (C2- is diamagnetic). - Statement 2 is incorrect (O2+ has a shorter bond length than O2). - Statement 3 is incorrect (N2+ and N2- do not have the same bond order). - Statement 4 is incorrect (Helium 2+ is not at the same energy as two isolated Helium atoms).
**Step-by-Step Solution:** 1. **Understanding Molecular Orbital Theory:** - Molecular Orbital (MO) theory explains how atomic orbitals combine to form molecular orbitals, which can be occupied by electrons. The key concepts include bonding and antibonding orbitals, bond order, and magnetic properties of molecules. 2. **Analyzing the Options:** - We have several statements to evaluate based on MO theory. We will analyze each statement one by one. ...
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