Final answer:
The 2s and 2py orbitals will not combine to form a molecular orbital due to the difference in their symmetries and the resulting zero net overlap integral, compounded by the energy difference between these orbitals.
Step-by-step explanation:
To demonstrate why a 2s and a 2py orbital will not combine to form a molecular orbital by evaluating their overlap integral over all space, one must consider the symmetry and orientation of the orbitals. Atomic orbitals can combine to form molecular orbitals if they have the same symmetry with respect to the internuclear axis and if their overlaps are energetically favorable. The overlap integral is a mathematical expression that quantifies the extent to which two orbitals overlap to form a molecular orbital with the overlap being constructive (adds electron density between the nuclei) or destructive (reduces electron density between the nuclei).
The 2s orbital is spherically symmetrical, meaning it can overlap equally well in all directions. In contrast, the 2py orbital is one of the p-orbitals which have two lobes with a nodal plane passing through the nucleus. The 2py is oriented perpendicular to the y-axis, and its nodal plane is in the xz plane. For effective overlap, atomic orbitals should have lobes with the same phase (sign) in the region of space between the nuclei. The phases of the 2s and 2py orbitals do not match in this way, leading to zero net overlap because the contributions of the orbital overlap cancel each other out in the integral calculus that describes this interaction.
This results from the symmetry of the 2s orbitals and the directional nature of the 2py orbitals. Therefore, combining a 2s orbital with a 2py orbital does not lead to effective orbital overlap, which means no bonding molecular orbital would form from these two atomic orbitals. Additionally, the energy difference between the 2s and 2p orbitals further complicates the issue, making the formation of such a molecular orbital energetically unfavorable. Therefore, the overlap integral for a 2s and a 2py combination will be effectively zero for all space.