Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 7

Relative to electrons and electron states, what does each of the four quantum numbers specify?

Short Answer

Expert verified
Answer: The four primary quantum numbers are the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s). The principal quantum number (n) represents an electron's energy level and average distance from the nucleus. The azimuthal quantum number (l) describes the shape of the electron's orbital within a given energy level. The magnetic quantum number (m_l) is related to the orientation of the electron's orbital in space relative to other orbitals in the atom. Lastly, the spin quantum number (m_s) describes the intrinsic angular momentum or "spin" of the electron.

Step by step solution

01

Introduce quantum numbers

Quantum numbers are used to describe the state and the arrangement of electrons in an atom. There are four primary quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s). Each of these quantum numbers has a specific meaning that helps to define the state of an electron within an atom.
02

Explain the principal quantum number (n)

The principal quantum number (n) represents an electron's energy level and its average distance from the nucleus. It can take on any positive integer value (n = 1, 2, 3, ...). As n increases, the electron is further from the nucleus and has higher energy. The value of n also determines the number of available electron orbitals within that energy level (e.g., for n=1, there is 1 orbital, and for n=2, there are 4 orbitals).
03

Explain the azimuthal quantum number (l)

The azimuthal quantum number (l) describes the shape of the electron's orbital within a given energy level. It can take on integer values from 0 to n-1. The value of l is often referred to as the orbital's angular momentum quantum number because it relates to the electron's angular momentum around the nucleus. The various values of l also correspond to specific letter designations: l = 0 is called an "s" orbital, l = 1 is a "p" orbital, l = 2 is a "d" orbital, and l = 3 is an "f" orbital.
04

Explain the magnetic quantum number (m_l)

The magnetic quantum number (m_l) is related to the orientation of the electron's orbital in space relative to the other orbitals in the atom. It can take on integer values from -l to +l (including zero). For example, if l = 2 (a "d" orbital), m_l can be -2, -1, 0, 1, 2, resulting in a total of 5 distinguishable "d" orbitals. The value of m_l determines the specific orbital within a given subshell (i.e., within the set of orbitals sharing the same values of n and l).
05

Explain the spin quantum number (m_s)

The spin quantum number (m_s) describes the intrinsic angular momentum or "spin" of the electron. It has only two possible values: +1/2 or -1/2. These two possible spins represent the "spin up" and "spin down" states of an electron. In any given orbital, there can be at most two electrons, one with a spin of +1/2 and one with a spin of -1/2. This is known as the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers.

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

The atomic radii of \(\mathrm{Mg}^{2+}\) and \(\mathrm{F}^{-}\)ions are \(0.072\) and \(0.133 \mathrm{~nm}\), respectively. (a) Calculate the force of attraction between these two ions at their equilibrium interionic separation (i.e., when the ions just touch one another). (b) What is the force of repulsion at this same separation distance?

For an \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)ion pair, attractive and repulsive energies \(E_{A}\) and \(E_{R}\), respectively, depend on the distance between the ions \(r\), according to $$ \begin{aligned} &E_{A}=-\frac{1.436}{r} \\ &E_{R}=\frac{7.32 \times 10^{-6}}{r^{8}} \end{aligned} $$ For these expressions, energies are expressed in electron volts per \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)pair, and \(r\) is the distance in nanometers. The net energy \(E_{N}\) is just the sum of the preceding two expressions. (a) Superimpose on a single plot \(E_{N}, E_{R}\), and \(E_{A}\) versus \(r\) up to \(1.0 \mathrm{~nm}\). (b) On the basis of this plot, determine (i) the equilibrium spacing \(r_{0}\) between the \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\) ions, and (ii) the magnitude of the bonding energy \(E_{0}\) between the two ions. (c) Mathematically determine the \(r_{0}\) and \(E_{0}\) values using the solutions to Problem 2.18, and compare these with the graphical results from part (b).

With regard to electron configuration, what do all the elements in Group IIA of the periodic table have in common?

Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride \((\mathrm{HCl})\left(19.4^{\circ} \mathrm{C}\right.\) vs. \(\left.-85^{\circ} \mathrm{C}\right)\), even though HF has a lower molecular weight.

(a) What electron subshell is being filled for the rare earth series of elements on the periodic table? (b) What electron subshell is being filled for the actinide series?
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Circular Motion and Gravitation

Read Explanation

Electric Charge Field and Potential

Read Explanation

Kinematics Physics

Read Explanation

Waves Physics

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