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), \((\mathrm{c})\) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

Short answer

In this problem, we have three overlap scenarios: (a) For the overlap between 2s orbitals on both atoms, we draw two overlapping spheres representing the 2s orbitals, with the shared region indicating electron density. (b) For the overlap of two 2pz orbitals, we draw two horizontally aligned dumbbell shapes on the z-axis, with the overlap happening between the facing lobes of the orbitals, resulting in a sigma bond along the z-axis. (c) For the overlap between a 2s orbital and a 2pz orbital, we draw a sphere for the 2s orbital and a horizontally aligned dumbbell for the 2pz orbital on the z-axis. The overlap occurs between one lobe of the 2pz and the sphere of the 2s orbital.

Step-by-step solution

Case (a): Overlap between 2s orbitals on both atoms

In this case, we consider two 2s orbitals, one on each atom. These s orbitals are spherical, with the center of the sphere corresponding to the nucleus of the respective atom. Step 1: Draw two overlapping spheres to represent the 2s orbitals on each atom. The overlap region indicates the electron density shared between the two atoms, leading to a covalent bond.

Case (b): Overlap between 2pz orbitals on both atoms

In this scenario, we need to examine the overlap between two 2pz orbitals, with each atom located on the z-axis. These orbitals are dumbbell-shaped, oriented along the z-axis. Step 1: Draw two horizontally aligned dumbbell shapes (2pz orbitals) on the z-axis, depicting their orientations. Step 2: Show the overlapping region in the middle where the electron density is shared. This overlap happens between the lobes of the two orbitals facing each other, resulting in a sigma bond along the z-axis.

Case (c): Overlap between 2s orbital on one atom and 2pz orbital on the other atom

This case involves the overlap between a 2s orbital on one atom and a 2pz orbital on the other atom. Keep in mind the 2s orbital is spherical, while the 2pz orbital is dumbbell-shaped and oriented along the z-axis. Step 1: Draw a sphere representing the 2s orbital on one atom and a horizontally aligned dumbbell on the z-axis for the 2pz orbital on the other atom. Step 2: Indicate the overlapping region between the 2s and 2pz orbitals, where the electron density is shared. The overlap occurs between one of the lobes of the 2pz orbital and the sphere corresponding to the 2s orbital.

Key concepts

2s Orbital

The 2s orbital is a region around an atom where there's a high probability of finding an electron. This orbital has a spherical shape, centered on the atom's nucleus. Think of it like a balloon that inflates around the nucleus and can hold up to two electrons.

When two atoms come close together, their 2s orbitals can overlap, sharing the space where their electrons exist. This overlap is spherical and therefore isotropic, meaning it's uniform in all directions. This shared region of electron density is what helps form a covalent bond, which we'll talk about in more detail later.

2pz Orbital

On the other hand, the 2pz orbital has a very different shape from the 2s. It's part of the p-orbital family and is distinguished by its dumbbell-shaped region of electron probability. This extends above and below (or along) the z-axis of an atom in a symmetrical fashion.

The 2pz orbital can hold two electrons, just like the 2s, but because of its shape, when it overlaps with another 2pz orbital on the z-axis, the shared space (where electron density pools) is also dumbbell-shaped. This type of overlap is directly along the axis where the p orbitals point, creating an optimal condition for a strong covalent bond.

Sigma Bond

A sigma bond, symbolized as \( \sigma \), is the strongest type of covalent bond. It occurs when two atomic orbitals overlap directly between the nuclei of atoms. Imagine two people sharing a handshake; the hands represent the orbitals and the firm grip, the electron density.

Be it between two s orbitals or two p orbitals (like the 2pz) or between an s and a p orbital, the sigma bond is always formed through the head-on or axial overlap, leading to a robust linkage between the atoms. In diagrams, the sigma bond is often depicted as a single line connecting the atomic symbols representing the nuclei.

Covalent Bonding

Covalent bonding is the sharing of electron pairs between atoms. These pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding.

In covalent bonds, the electron density shared between atoms in orbitals is what keeps them together. Simple representations use dots and lines to show where the electrons are, but in reality, it's more like a tug-of-war where both atoms hold onto the electrons, creating a balanced and stable bond. This concept is fundamental to understanding how molecules form and hold together.

Electron Density

Electron density refers to the probability of electrons being present in a particular region around an atom. Higher electron density areas are often where bonds form, since electrons are the glue that holds atoms together.

When sketching orbitals, the darker or more concentrated regions indicate where there is a higher likelihood of finding electrons. In bonding, especially covalent bonding, the electron density concentrates between the nuclei, allowing for various kinds of orbital overlap. This concentration of electrons is what creates the bond and gives the molecule its shape and stability.