Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 64

Sketch the shape and orientation of the following types of orbitals: (a) \(p_{x},(\mathbf{b}) d_{2}^{2},(\mathbf{c}) d_{x^{2}-y^{2}}\)

Short Answer

Expert verified
(a) The px orbital has a dumbbell shape, with one lobe on the positive x side and the other on the negative x side of a Cartesian coordinate system. (b) The d₂² orbital has a "four-leaf clover" shape, with lobes placed diagonally between the x, y, and z axes, specifically in the positive-x positive-y, negative-x positive-y, negative-x negative-y, and positive-x negative-y regions. (c) The dx²-y² orbital has a "four-leaf clover" shape similar to d₂², but with lobes aligned along the x and y axes, with one lobe in the positive-x, negative-x, positive-y, and negative-y regions.

Step by step solution

01

(a) Sketching px Orbital

: To sketch the px orbital, we need to recall that p orbitals have a dumbbell shape. The px orbital is aligned along the x-axis. 1. Draw the x, y, and z-axis on a Cartesian coordinate system. 2. Now sketch a dumbbell shape centered on the x-axis, with one lobe on the positive x side and the other on the negative x side. 3. Label the orbital as px.
02

(b) Sketching d₂² Orbital

: To sketch the d₂² orbital, recall that d orbitals have a complex "four-leaf clover" shape. The orientation of d₂² will lie along the x, y, and z axes. 1. Draw the x, y, and z-axis on a Cartesian coordinate system. 2. Visualize the d₂² clover-like shape with four lobes placed diagonally between the x, y, and z axes. One lobe should be in the positive-x positive-y region, one in the negative-x positive-y region, one in the negative-x negative-y region, and one in the positive-x negative-y region. 3. Label the orbital as d₂².
03

(c) Sketching dx²-y² Orbital

: To draw the dx²-y² orbital, which is also a type of d orbital, recall that d orbitals have a complex "four-leaf clover" shape. The shape of the dx²-y² orbital is similar to that of d₂², but with its lobes aligned along the x and y axes. 1. Draw the x, y, and z-axis on a Cartesian coordinate system. 2. Visualize the dx²-y² clover-like shape by placing four lobes around the axis with two lobes aligned along the x-axis and the other two lobes aligned along the y-axis. One lobe should be in the positive-x region, one in the negative-x region, one in the positive-y region, and one in the negative-y region. 3. Label the orbital as dx²-y².

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Bohr's model can be used for hydrogen-like ions-ions that have only one electron, such as \(\mathrm{He}^{+}\) and \(\mathrm{Li}^{2+} .\) (a) Why is the Bohr model applicable to He \(^{+}\) ions but not to neutral He atoms? (b) The ground-state energies of \(\mathrm{H}, \mathrm{He}^{+},\) and \(\mathrm{Li}^{2+}\) are tabulated as follows: $$ \begin{array}{l}{\text { Atom or ion } \quad \quad\quad\quad\quad\quad \mathrm{H} \quad\quad\quad\quad\quad\quad \text { He }^{+} \quad\quad\quad\quad\quad\quad\quad \mathrm{Li}^{2+}} \\ {\text { Ground- state }\quad-2.18 \times 10^{-18} \mathrm{J}\quad-8.72 \times 10^{-18} \mathrm{J}\quad-1.96 \times 10^{-17} \mathrm{J}} \\ {\text { energy }}\end{array} $$ By examining these numbers, propose a relationship between the ground-state energy of hydrogen-like systems and the nuclear charge, \(Z .(\mathbf{c})\) Use the relationship you derive in part (b) to predict the ground-state energy of the \(\mathrm{C}^{5+}\) ion.

Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 \(\mathrm{m} / \mathrm{s}\) if the speed is known to within \(\pm 0.01 \mathrm{m} / \mathrm{s}\) ; (b) a proton moving at a speed of \((5.00 \pm 0.01) \times 10^{4} \mathrm{m} / \mathrm{s}\) . (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)

(a) What is the relationship between the wavelength and the frequency of radiant energy? (b) Ozone in the upper atmosphere absorbs energy in the \(210-230-\mathrm{nm}\) range of the spectrum. In what region of the electromagnetic spectrum does this radiation occur?

Classify each of the following statements as either true or false: (a) A hydrogen atom in the \(n=3\) state can emit light at only two specific wavelengths, (b) a hydrogen atom in the \(n=2\) state is at a lower energy than one in the \(n=1\) state, and (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free