When two 2p_z orbitals (assuming z is the internuclear axis) overlap, they form sigma ($\sigma$) and sigma antibonding (${\sigma }^{\ast }$) molecular orbitals.

Concept: Nodal Planes in Molecular Orbitals

A nodal plane is a plane where the probability of finding an electron is zero. For molecular orbitals formed from p-orbitals, the number and orientation of nodal planes are crucial for understanding their properties.

Why (A) is correct:

When two 2p_z orbitals overlap along the z-axis, the resulting ${\sigma }_{2p_z}$ bonding molecular orbital has two nodal planes. One nodal plane is the xy-plane (perpendicular to the internuclear axis, passing through the center), and the other is the yz-plane (containing the internuclear axis). These arise from the original p-orbitals' nodal planes.

Option Analysis:

• A) $\sigma$ orbital has a total of two nodal planes: This is correct. The ${\sigma }_{2p_z}$ bonding orbital has two nodal planes: one perpendicular to the internuclear axis (xy-plane) and one containing the internuclear axis (yz-plane).
• B) ${\sigma }^{\ast }$ orbital has one node in the xz-plane containing the molecular axis: This is incorrect. The ${\sigma }^{\ast }$ antibonding orbital formed from 2p_z orbitals has one nodal plane perpendicular to the internuclear axis (the xy-plane) between the two nuclei, and also the yz-plane and xz-plane (containing the internuclear axis) from the original p-orbitals.
• C) $\pi$ orbital has one node in the plane which is perpendicular to the molecular axis and goes through the center of the molecule: This is incorrect. $\pi$ orbitals are formed by the sideways overlap of p-orbitals (e.g., 2p_x with 2p_x or 2p_y with 2p_y). A $\pi$ bonding orbital has one nodal plane that contains the internuclear axis (e.g., the yz-plane for overlap of 2p_x orbitals). It does not have a nodal plane perpendicular to the molecular axis passing through the center.
• D) ${\pi }^{\ast }$ orbital has one node in the xy-plane containing the molecular axis: This is incorrect. A ${\pi }^{\ast }$ antibonding orbital has two nodal planes: one containing the internuclear axis (e.g., the yz-plane for 2p_x overlap) and another perpendicular to the internuclear axis between the nuclei. The xy-plane is perpendicular to the z-axis, so it would not contain the molecular axis if the molecular axis is z.

Correct Answer: (A)