Question

Sketch the shape and orientation of the following types of orbitals: \((\mathbf{a}) s,(\mathbf{b}) p_{z},(\mathbf{c}) d_{x y}\).

Short answer

The s orbital is spherical with no specific orientation. The p_z orbital has a dumbbell shape along the z-axis, with two lobes connected by a nodal plane. The d_xy orbital has four lobes in the xy plane, forming an "X" shape when viewed from above.

Step-by-step solution

Sketch the s orbital

The s orbital is the simplest of all types of orbitals. It is spherical in shape, with the nucleus of the atom at the center. The s orbital doesn't have any specific orientation since it is symmetrical in all three dimensions. When sketching, draw a small circle to represent the nucleus, and then a larger circle around it that represents the s orbital. The space inside the large circle is where the electron is most likely to be found.

Sketch the p_z orbital

The p_z orbital is one of the three p orbitals. It has a dumbbell shape along the z-axis. To sketch the p_z orbital, draw the nucleus, and then two lobes (oval shapes) above and below the nucleus, representing the regions with a high probability of finding the electron. The lobes should be connected by a thin line that represents the nodal plane, which is an area with minimal likelihood of finding the electron. Label the vertical axis as 'z', showing that the orbital lies along this axis.

Sketch the d_xy orbital

The d_xy orbital is a d orbital and has a more complex shape. It consists of four lobes located in the xy plane, with each lobe pointing towards the corners of the x and y axes. To sketch the d_xy orbital, draw the nucleus and then add four lobes in the xy plane with two lobes on either side of the nucleus. These lobes should form an "X" shape when viewed from above. Label the axes as 'x' and 'y' to show that the orbital lies in the xy plane.

Key concepts

s orbital

The s orbital is the most basic type of atomic orbital you might encounter. It is unique because it is perfectly spherical in shape. This means that it looks like a ball and is the same in all directions, which is described as having spherical symmetry. Since it is centered around the nucleus of the atom, its size only changes depending on the energy level it belongs to.
What makes the s orbital easy to understand is that it doesn't have a preferred direction in space. Because of its symmetry, it holds electrons in a cloud-like distribution around the nucleus.

• Its shape is like a simple ball, with a uniform distribution of electron density.
• No nodal planes in the simplest form, which means there's no imaginary surface where the probability of finding an electron is zero inside the main ball.
• All s orbitals, regardless of size, share this same shape.

S orbitals are essential in chemistry because they are the first orbitals filled as atoms build up their electron configuration. This characteristic makes them foundational in understanding more complex geometries as electrons populate higher energy levels.

p orbital

The p orbitals start to introduce a bit more complexity with their distinctive dumbbell shape. Unlike the s orbital, the p orbital is not spherical but more elongated. It features two lobes, one on each side of the nucleus, creating a structure somewhat like a dumbbell or a peanut.
These orbitals come in three distinct orientations: along the x, y, and z axes of an atom, denoted as p_x, p_y, and p_z, respectively. This arrangement helps accommodate more electrons as they fill up these regions of space according to the electron configuration of an element.

• Each p orbital has a nodal plane that goes through the nucleus, creating a region where electron likelihood is nearly zero.
• The three orientations (p_x, p_y, and p_z) help maximize the space for electrons around the nucleus.
• The two lobes mean that electrons can be found high in these regions relative to the nucleus.

Understanding p orbitals is crucial as they explain a wide range of chemical bonding and molecular geometry. From participating in hybridization to forming pi bonds, p orbitals play a pivotal role in the behavior of atoms in molecules.

d orbital

The d orbitals take complexity to the next level, featuring elaborate shapes and surfaces. There are five different d orbitals: d_xy, d_xz, d_yz, d_x^2-y^2, and d_z^2. Each has its unique orientation but here we will focus on the d_xy orbital.
This particular orbital is characterized by its four-lobed structure. The lobes are arranged in the xy plane, each oriented between the axis lines, giving it an "X" shape when viewed down the z-axis. This is one of the signature features of d orbitals: their complexity increases due to multiple lobes and specific orientations.

• Each of the five d orbitals has its own orientation scheme, which allows d electrons to occupy space differently.
• Nodal planes are more prominent in d orbitals, contributing to their complex shape.
• The involvement of d orbitals is key in transition metals and explains much of their unique chemistry, including color and magnetism.

With their advanced nature, d orbitals hold significant importance in inorganic chemistry and play a vital role in understanding the properties and behaviors of complex molecules and metals.