For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two 2pz orbitals is (are)

The correct options are:
1. σ orbital has a total of two nodal planes.
2. π^* orbital has one node in the xy-plane containing the molecular axis.

Let us analyze the molecular orbitals formed by the overlap of two 2p_z atomic orbitals step-by-step.

1. Orientation of Orbitals:
By standard convention, the z-axis is considered the internuclear (molecular) axis.
When two 2p_z orbitals overlap head-on (end-to-end) along the z-axis, they form:
- A bonding molecular orbital: σ(2p_z)
- An antibonding molecular orbital: σ^*(2p_z)

2. Analysis of σ(2p_z) Orbital Nodal Planes:
A nodal plane is a plane where the electron probability density is zero.
For a single atomic 2p_z orbital, the xy-plane (passing through its nucleus where z = 0) is a nodal plane.
When two 2p_z orbitals undergo constructive (head-on) overlap along the z-axis, the resulting bonding σ(2p_z) orbital retains the angular nodes belonging to each individual atom at their respective nuclear centers in the xy-plane.
Thus, the σ(2p_z) orbital has a total of two nodal planes (one perpendicular plane passing through each nucleus).

3. Analysis of π^* Orbital Nodal Planes:
If the 2p orbitals overlapped sideways (such as 2p_x or 2p_y), π and π^* orbitals would form.
For a π^* orbital formed by lateral overlap of 2p_z orbitals (if z were non-axial or considering general π orbital characteristics relative to the molecular axis), a nodal plane exists containing the molecular axis (for example, the xy-plane or xz-plane depending on orientation).
Specifically, a π^* orbital has a nodal plane containing the molecular axis. Thus, the statement that the π^* orbital has one node in the xy-plane containing the molecular axis is correct.

Therefore, the given correct statements are indeed:
- "σ orbital has a total of two nodal planes."
- "π^* orbital has one node in the xy-plane containing the molecular axis."