Azimuthal quantum number | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_l, and the spin quantum number m_s). It is also known as the orbital angular momentum quantum number, orbital quantum number, subsidiary quantum number, or second quantum number, and is symbolized as l (pronounced ell). Connected with the energy states of the atom's electrons are four quantum numbers: n, l, ml, and ms. These specify the complete, unique quantum state of a single electron in an atom, and make up its wavefunction or orbital. When solving to obtain the wave function, the Schrödinger equation reduces to three equations that lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The azimuthal quantum number arose in the solution of the polar part of the wave equation as shown below , reliant on the spherical coordinate system, which generally works best with models having some glimpse of spherical symmetry. An atomic electron's angular momentum, L, is related to its quantum number l by the following equation: where ħ is the reduced Planck's constant, L2 is the orbital angular momentum operator and is the wavefunction of the electron. The quantum number l is always a non-negative integer: 0, 1, 2, 3, etc. L has no real meaning except in its use as the angular momentum operator. When referring to angular momentum, it is better to simply use the quantum number l. Atomic orbitals have distinctive shapes denoted by letters. In the illustration, the letters s, p, and d (a convention originating in spectroscopy) describe the shape of the atomic orbital. Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related concepts (52)

Related courses (16)

Related lectures (130)

Related MOOCs (1)

Spin quantum number

In physics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1/2 for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written ms.

Azimuthal quantum number

Principal quantum number

In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number l, the magnetic quantum number ml, and the spin quantum number s. As n increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus.

CH-110: Advanced general chemistry I

Le cours comporte deux parties. Les bases de la thermodynamique des équilibres et de la cinétique des réactions sont introduites dans l'une d'elles. Les premières notions de chimie quantique sur les é

CH-244: Quantum chemistry

Introduction to Quantum Mechanics with examples related to chemistry

PHYS-101(g): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3

Henrik Moodysson Rønnow, Martin Mourigal, Jean-Sebastien Caux, Thorsten Schmitt

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic o

2012

Basic Steps in Magnetic Resonance

A MOOC to discover basic concepts and a wide range of intriguing applications of magnetic resonance to physics, chemistry, and biology

Discusses quantum particles interaction, confinement, and potential energy in confined spaces.

Explores the angular momentum theorem in gyroscope dynamics and symmetrical motion.

Covers the concept of quantum computation delegation and the relationship between MIP and RE, addressing common FAQs and discussing helpful materials and interactions with quantum devices.