/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 An electron in an atom is in the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 54

An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.

Short Answer

Expert verified
For the third quantum level (\(n = 3\)), the possible combinations of \(\ell\) and \(m_{\ell}\) are: (\(0, 0\)), (\(1, -1\)), (\(1, 0\)), (\(1, 1\)), (\(2, -2\)), (\(2, -1\)), (\(2, 0\)), (\(2, 1\)), (\(2, 2\)).

Step by step solution

01

Determine the possible values of \(\ell\)

The azimuthal quantum number \(\ell\) can have integer values ranging from 0 to \(n-1\). Here, with \(n = 3\), the possible values of \(\ell\) can be 0, 1, or 2.
02

Determine the possible values of \(m_{\ell}\) for each \(\ell\)

For each value of \(\ell\), \(m_{\ell}\) can have integer values ranging from \(-\ell\) to \(\ell\). Consequently, when \(\ell = 0\), \(m_{\ell} = 0\); when \(\ell = 1\), \(m_{\ell}\) can be \(-1, 0, 1\); and when \(\ell = 2\), \(m_{\ell}\) can be \(-2, -1, 0, 1, 2\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

List the hydrogen orbitals in increasing order of energy.

The sun is surrounded by a white circle of gaseous material called the corona, which becomes visible during a total eclipse of the sun. The temperature of the corona is in the millions of degrees Celsius, which is high enough to break up molecules and remove some or all of the electrons from atoms. One way astronomers have been able to estimate the temperature of the corona is by studying the emission lines of ions of certain elements. For example, the emission spectrum of \(\mathrm{Fe}^{14+}\) ions has been recorded and analyzed. Knowing that it takes \(3.5 \times 10^{4} \mathrm{~kJ} / \mathrm{mol}\) to convert \(\mathrm{Fe}^{13+}\) to \(\mathrm{Fe}^{14+},\) estimate the temperature of the sun's corona.

Use the Aufbau principle to obtain the ground-state electron configuration of technetium.

(a) What is the frequency of light having a wavelength of \(456 \mathrm{nm} ?\) (b) What is the wavelength (in nanometers) of radiation having a frequency of \(2.45 \times 10^{9} \mathrm{~Hz} ?\) (This is the type of radiation used in microwave ovens.)

The blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a frequency of about \(7.5 \times 10^{14} \mathrm{~Hz}\). (a) Calculate the wavelength, in \(\mathrm{nm}\), associated with this radiation, and (b) calculate the energy, in joules, of a single photon associated with this frequency.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

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.