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Ch.6 - Electronic Structure of Atoms
All textbooksBrown 15th EditionCh.6 - Electronic Structure of AtomsProblem 64
Chapter 6, Problem 64

Sketch the shape and orientation of the following types of orbitals: (a) px, (b) dz2, (c) dx2 - y2.

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Understand that the d orbitals are a set of five orbitals in the third energy level and higher, each with a unique shape and orientation.
Recognize that the \(d_{x^2 - y^2}\) orbital is one of these five d orbitals, characterized by its distinct shape.
Visualize the \(d_{x^2 - y^2}\) orbital as having four lobes oriented along the x and y axes, forming a cloverleaf shape.
Note that the lobes of the \(d_{x^2 - y^2}\) orbital lie in the xy-plane, with the nodal planes along the x = 0 and y = 0 lines, meaning there is no electron density along these lines.
Remember that the orientation of the \(d_{x^2 - y^2}\) orbital is crucial for understanding its role in chemical bonding, particularly in transition metal complexes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. They are defined by quantum numbers and have distinct shapes, such as s, p, d, and f orbitals. Each type of orbital has a specific geometric configuration that influences the chemical properties of the atom.
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Atomic Orbitals Example

d-Orbitals

d-orbitals are a set of five orbitals that are more complex in shape compared to s and p orbitals. They are important for transition metals and can hold a maximum of ten electrons. The dx2 - y2 orbital, in particular, has a unique shape that resembles a four-leaf clover, oriented along the x and y axes.
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Orbital Orientation

Orbital orientation refers to the spatial arrangement of orbitals in relation to the axes of a coordinate system. For the dx2 - y2 orbital, its lobes are oriented along the x and y axes, with nodal planes along the diagonals. Understanding this orientation is crucial for predicting molecular geometry and bonding behavior in chemistry.
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Related Practice
Textbook Question

Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d

Textbook Question

For the table that follows, write which orbital goes with the quantum numbers. Don't worry about x, y, z subscripts. If the quantum numbers are not allowed, write 'not allowed.' n l ml Orbital 2 1 -1 2p (example) 1 0 0 3 -3 2 3 2 -2 2 0 -1 0 0 0 4 2 1 5 3 0

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Textbook Question

Sketch the shape and orientation of the following types of orbitals: (a) s, (b) pz, (c) dxy.

Textbook Question

(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number?

Textbook Question

(a) For an He+ ion, do the 2s and 2p orbitals have the same energy? If not, which orbital has a lower energy?

Textbook Question

(b) If we add one electron to form the He atom, would your answer to part (a) change?