The `sigma_(2s)` orbital has a higher energy than `sigma_(1s)^(**)` orbital, `sigma(_2s)` orbital is bonding while `sigma_(1s)^(**)` orbital is antibonding because :

Options

A. `sigma_(2s)` is planar while `sigma_(1s)^(**)` orbital.
B. `sigma_(2s)` is symmetrical while `sigma_(1s)^(**)` is unsymmetrical
C. `sigma_(2s)` is nearer to the nuclei than `sigma_(1s)^(**)`
D. none of these

Answer

To solve the question regarding the energy levels and bonding characteristics of the `sigma_(2s)` and `sigma_(1s)^(**)` orbitals, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Molecular Orbitals (MOs)**:
- Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO). They can be classified into bonding and antibonding orbitals.
- Bonding orbitals are lower in energy and are formed when atomic orbitals combine constructively, while antibonding orbitals are higher in energy and are formed when atomic orbitals combine destructively.

2. **Identify the Orbitals**:
- The `sigma_(1s)` orbital is a bonding molecular orbital formed from the combination of 1s atomic orbitals.
- The `sigma_(1s)^(**)` orbital is an antibonding molecular orbital, denoted by the asterisk (*), which has higher energy than the bonding orbital.
- The `sigma_(2s)` orbital is another bonding molecular orbital formed from the combination of 2s atomic orbitals.

3. **Energy Comparison**:
- According to the molecular orbital theory, as we move to higher principal quantum numbers (n), the energy of the orbitals increases. Therefore, the `sigma_(2s)` orbital has higher energy than the `sigma_(1s)^(**)` orbital.
- The `sigma_(2s)` orbital is a bonding orbital, while the `sigma_(1s)^(**)` is an antibonding orbital.

4. **Symmetry Consideration**:
- The `sigma_(2s)` orbital is symmetrical in nature, which contributes to its bonding characteristics. It allows for effective overlap of atomic orbitals, leading to a stable bond.
- In contrast, the `sigma_(1s)^(**)` orbital is unsymmetrical, which leads to destructive interference between the wave functions of the atomic orbitals, resulting in an antibonding character.

5. **Conclusion**:
- Therefore, the `sigma_(2s)` orbital is bonding and has higher energy than the `sigma_(1s)^(**)` orbital, which is antibonding due to its unsymmetrical nature.

### Final Answer:
The `sigma_(2s)` orbital has a higher energy than `sigma_(1s)^(**)` because the `sigma_(2s)` orbital is symmetrical (bonding), while the `sigma_(1s)^(**)` orbital is unsymmetrical (antibonding).

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