Show how two \(2 p\) atomic orbitals can combine to form a \(\sigma\) or a \(\pi\) molecular orbital.

Short Answer

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Two 2p atomic orbitals can combine to form a σ (sigma) or a π (pi) molecular orbital based on their orientation and the type of overlap. A σ molecular orbital forms from the end-to-end overlap of 2p_z orbitals along the internuclear axis, resulting in electron density along the axis with constructive interference between the nuclei. In contrast, a π molecular orbital forms from the side-by-side overlap of 2p_x or 2p_y orbitals, creating electron density above and below the internuclear axis.

Step by step solution

01

Understanding atomic orbitals

2p atomic orbitals are "p" orbitals, meaning they have a dumbbell shape along the x, y, and z axes. There are three orbitals in the 2p subshell: 2p_x, 2p_y, and 2p_z, each oriented along a different axis. Every atomic orbital can hold up to 2 electrons with opposite spins.
02

Constructive and destructive interference

When atomic orbitals overlap, they can do so in either a constructive or destructive manner. Constructive interference occurs when the wavefunctions of the orbitals have the same sign (either both positive or both negative) and combine to give a higher electron density between the nuclei. This leads to the formation of a bonding molecular orbital. Destructive interference occurs when the wavefunctions of the orbitals have opposite signs (one positive and one negative), which leads to a lower electron density between the nuclei and the formation of an antibonding molecular orbital.
03

Formation of σ (sigma) molecular orbital

A sigma (σ) molecular orbital forms when two atomic orbitals overlap along the internuclear axis (the axis connecting the two nuclei). In this case, when two 2p_z orbitals overlap end-to-end along the internuclear axis, the electron density lies along the axis with constructive interference between the nuclei. The resulting orbital is cylindrically symmetrical and is called a σ (sigma) molecular orbital.
04

Formation of π (pi) molecular orbital

A pi (π) molecular orbital forms when two atomic orbitals overlap side-by-side, with the electron density occupying the space above and below the internuclear axis. When two 2p atomic orbitals, such as 2p_x or 2p_y, overlap side-by-side, the electron density is found in two regions, above and below the internuclear axis. This type of orbital is referred to as a π (pi) molecular orbital. In conclusion, two 2p atomic orbitals can combine in different ways to form a sigma (σ) or pi (π) molecular orbital, depending on their orientation and the type of overlap that occurs. Sigma orbitals form when the overlap occurs along the internuclear axis, while pi orbitals form when the overlap happens side-by-side with the electron density above and below the axis.

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