Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 64

Chapter 6, Problem 64

Sketch the shape and orientation of the following types of orbitals: (a) p_x, (b) d_z2, (c) d_{x2 - y2}.

Verified step by step guidance

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.

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.

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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d Orbital Orientations

Related Practice

Textbook Question

(d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.

Textbook Question

(c) What can you say about the average distance from the nucleus of an electron in a 2s orbital as compared with a 3s orbital?

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) p_z, (c) d_xy.

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

Verified video answer for a similar problem:

Key Concepts

Atomic Orbitals

d-Orbitals

Orbital Orientation

Sketch the shape and orientation of the following types of orbitals: (a) p_x, (b) d_z2, (c) d_{x2 - y2}.