Question

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the 2 s orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the z-axis), (c) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

Short answer

To sketch the overlap between the given atomic orbitals, follow these steps: 1. Review the shapes of atomic orbitals: 2s orbitals are spherical and symmetrical, while 2p_z orbitals are dumbbell-shaped and oriented along the z-axis. 2. Overlap between 2s orbitals on both atoms: Draw two spheres representing 2s orbitals with a lens-shaped overlap region between them. 3. Overlap between 2 p_z orbitals on both atoms: Draw two dumbbell-shaped orbitals oriented along the z-axis with overlapping positive and negative lobes, resulting in two regions of overlap in a linear configuration along the z-axis. 4. Overlap between the 2s and 2 p_z orbitals on the two atoms: Draw a spherical 2s orbital on one atom and a dumbbell-shaped 2 p_z orbital on the other atom, with a lens-shaped overlap between the 2s orbital and the positive lobe of the 2 p_z orbital.

Step-by-step solution

Review the shapes of atomic orbitals

Before we start sketching, let's quickly review the basic shapes of the atomic orbitals involved in the exercise. - The 2s orbitals are spherical and symmetrical. They are the second energy level of the s orbitals and contain one radial node. - The 2p orbitals are dumbbell-shaped with one positive and one negative lobe. The p orbitals have three possible orientations in space: 2p_x, 2p_y, and 2p_z. In this exercise, we are specifically dealing with the 2 p_z orbitals, which are vertically oriented along the z-axis. Now that we have a clear understanding of the shapes of the orbitals, let's create the sketches for the overlaps.

Sketch the overlap between the 2s orbitals on both atoms

To sketch this configuration, draw two spheres representing the 2s orbitals on each atom. Place the spheres such that their centers are at a distance that allows for an overlap region between them. This overlap region should appear like a lens-shaped area where the two spheres are combined.

Sketch the overlap between the 2 p_z orbitals on both atoms

For this configuration, we need to draw two dumbbell-shaped orbitals with their positive and negative lobes oriented along the z-axis. Position the two atoms such that the positive lobe of one 2 p_z orbital overlaps with the positive lobe of the other 2 p_z orbital and similarly, the negative lobes overlap with each other. As a result, you should see two regions of overlaps, one positive and one negative, in a linear configuration along the z-axis.

Sketch the overlap between the 2s and 2 p_z orbitals on the two atoms

In this final situation, draw a 2s orbital as a sphere on one atom and a 2 p_z orbital as a dumbbell-shaped orbital on the other atom, with its positive lobe along the z-axis. Position the two atoms to create an overlap region between the 2s orbital and the positive lobe of the 2 p_z orbital, with a lens-shaped overlap between them. These sketches should now illustrate the different ways in which the given atomic orbitals overlap in the three scenarios.

Key concepts

2s Orbitals

When studying chemistry, the concept of 2s orbitals is fundamental to understanding how atoms bond and form molecules. The 2s orbital is one of the simplest structures encountered in quantum chemistry. It is part of the second principal energy level and shaped like a sphere, representing areas where electrons are most likely to be found. Unlike the 1s orbital, the 2s has a slightly larger radius and contains what is known as a radial node — a region where there is a zero probability of finding an electron.

Visually, when we draw the 2s orbital, it looks like a uniformly shaded sphere. When two 2s orbitals overlap, as in the covalent bonding between two atoms, they create a lens-shape overlap region in the space between the atomic nuclei. This type of overlap is conducive to the formation of a sigma bond, a strong covalent bond characterized by head-on orbital overlap.

2p_z Orbitals

The 2p_z orbitals are another class of atomic orbitals crucial for the formation of molecular structures. A 2p_z orbital is characterized by its figure-eight or dumbbell shape, with two lobes located along the z-axis, one extending in the positive direction and the other in the negative direction. Each lobe represents a region of high electron probability, with the center, or node, being a region of zero electron probability.

In illustrations, these orbitals are typically shown as two elliptical lobes on opposite sides of the nucleus. During the overlap of two 2p_z orbitals from adjacent atoms, the alignment along the z-axis allows the like-phased (same sign, positive or negative) lobes to overlap. This interaction can create a pi bond, especially when the lobes are parallel and next to one another, or reinforce the sigma bond in the case of end-to-end overlap. The proper alignment and overlap of these orbitals are essential for the formation of double and triple bonds.

Orbital Shapes

The shape of an atomic orbital is a visual representation of the regions in space where an electron is likely to be found most of the time. Orbitals come in various shapes, including the spherical 2s orbitals and the dumbbell-shaped 2p orbitals. The different shapes correspond to different energy states and orientations of the orbital in space.

Understanding orbital shapes is critical when predicting how atomic orbitals overlap to form molecular orbitals during bonding. The overlap pattern directly influences the strength and type of the chemical bond. For instance, spherical orbitals like the 2s typically form sigma bonds through head-on overlap, whereas the orientation-specific 2p orbitals can form pi bonds in addition to sigma bonds, depending heavily on the directional nature of their shapes.

Molecular Orbitals

Molecular orbitals are formed when atomic orbitals from individual atoms merge as the atoms come close enough to bond. This concept is central to molecular orbital theory, which explains the electron distribution in a molecule and how bonding occurs. There are two main types of molecular orbitals that can result from the overlap of atomic orbitals: bonding and antibonding orbitals.

Bonding molecular orbitals are lower in energy than the original atomic orbitals and are associated with the stability of the molecule. Meanwhile, antibonding orbitals are higher in energy and can lead to instability if they are occupied by electrons. The constructive overlap of atomic orbitals, such as two 2s or two 2p_z orbitals, results in the formation of bonding molecular orbitals, contributing to the stability and bonding of the molecule. By visualizing and understanding molecular orbitals, scientists can predict the behavior and properties of molecules.