Question

The energy of \(2 \mathrm{~s}\) is greater than \(\sigma^{*} 1 \mathrm{~s}\) orbital because (1) \(\sigma 2 \mathrm{~s}\) -orbital is bigger than \(\sigma\) /s-orbital. (2) \(\sigma 2 \mathrm{~s}\) is a bonding orbital, whereas \(\left.\sigma^{*}\right] \mathrm{s}\) an antibonding orbital. (3) \(\sigma 2 \mathrm{~s}\) orbital has a greater value of \(n\) that \(\sigma * 2 \mathrm{~s}\) -orbital. (4) \(\sigma 2 \mathrm{~s}\) orbital is formed only after \(\sigma \mid \mathrm{s}\).

Short answer

(2) \(\sigma 2s\) is a bonding orbital, whereas \(\sigma^* 1s\) is an antibonding orbital.

Step-by-step solution

Understand the concepts

First, review the concepts of bonding and antibonding orbitals. Bonding orbitals (like \(\sigma 2s\)) result from the constructive interference of atomic orbitals, leading to higher electron density between nuclei and a lower energy state. Antibonding orbitals (like \(\sigma^* 1s\)) result from the destructive interference of atomic orbitals, causing nodes between nuclei and a higher energy state.

Compare Bonding vs. Antibonding

Since \(\sigma 2s\) is a bonding orbital and \(\sigma^* 1s\) is an antibonding orbital, we can conclude that the energy of a bonding orbital is always less than that of an antibonding orbital. Therefore, \(\sigma 2s\) should naturally have lower energy than \(\sigma^* 1s\).

Analyze the options

Now analyze the provided options: 1. \(\sigma 2s\) being bigger than \(\sigma 1s\) is not directly related to energy. 2. \(\sigma 2s\) being bonding and \(\sigma^* 1s\) being antibonding is correct. 3. The principal quantum number \(n \) difference does not affect the specific energy comparison between these two orbitals here. 4. Formation order does not directly relate to energy comparison of \(\sigma 2s\) and \(\sigma^* 1s\).

Conclusion

The correct answer based on the analysis is the statement that \(\sigma 2s\) is a bonding orbital, whereas \(\sigma^* 1s\) is an antibonding orbital.

Key concepts

bonding orbitals

Bonding orbitals are formed when atomic orbitals combine constructively. This means that the wave functions of the atomic orbitals add together. The result is an orbital with greater electron density between the two nuclei.
This increase in electron density creates an attractive force that holds the atoms together. This attractive force lowers the energy of the system, making the bonding orbital a low-energy, more stable arrangement.
Some key characteristics of bonding orbitals:

• They stabilize the molecule
• They have increased electron density between the nuclei
• They are characterized by lower energy than the original atomic orbitals

antibonding orbitals

Antibonding orbitals are quite different from bonding orbitals. These result from the destructive interference of atomic orbitals.
This means that the wave functions of the atomic orbitals subtract from each other. The result is an orbital with a node or region of zero electron density between the two nuclei.

• Nodes are areas where the probability of finding an electron is zero.
• This lack of electron density creates a repulsive force between the atomic nuclei.

This repulsive force increases the energy of the system, making the antibonding orbital a high-energy, and less stable arrangement.
Some key characteristics of antibonding orbitals:

• They destabilize the molecule
• They have a node between the nuclei
• They are characterized by higher energy than the original atomic orbitals

molecular orbital theory

Molecular Orbital (MO) Theory provides a more accurate description of molecular bonding compared to Valence Bond Theory. In MO Theory, atomic orbitals combine to form molecular orbitals which span the entire molecule. There are two types of molecular orbitals that can be formed: bonding and antibonding orbitals.
Some key points of MO Theory:

• Atomic orbitals combine to form molecular orbitals.
• Molecular orbitals are spread over several atoms in a molecule.
• Electron configuration in molecular orbitals dictates the chemical and physical properties of the molecule.

MO Theory helps explain phenomena such as the bond order, magnetic properties, and stability of molecules.

electron density

Electron density refers to the probability of finding an electron in a particular region around the nucleus. It is a crucial concept for understanding bonding and antibonding orbitals.

• High electron density between two nuclei stabilizes the molecule, forming a bonding orbital.
• Low or zero electron density between two nuclei destabilizes the molecule, forming an antibonding orbital (due to the presence of a node).

By studying electron density, chemists can predict and explain the stability and reactivity of various molecules. High electron density regions indicate areas of significant bonding interactions, whereas nodes or areas of low electron density indicate repulsive or destabilizing interactions.