ELECTRONS AND QUANTUM NUMBERS - A quantum number is a value that is used when describing the energy levels available to atoms and molecules. An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom. While quantum numbers are commonly used to describe electrons, they may be used to describe the nucleons (protons and neutrons) of an atom or elementary particles.

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Electrons And Quantum Numbers

Quantum Number Definition

by Anne Marie Helmenstine, Ph.D.

A quantum number is a value that is used when describing the energy levels available to atoms and molecules.

An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom.

There are four quantum numbers:

·       n – principal quantum number - describes the energy level

·       ℓ - azimulhal or angular momentum quantum number - describes the subshell

·       m_ℓ or m - magnetic quantum number - describes the orbital of the subshell

·       m_s or s – spin quantum number - describes the spin

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Quantum Number Values

According to the Pauli exclusion principle, no two electrons in an atom can have the same set of quantum numbers.

Each quantum number is represented by either a half-integer or integer value.

·     The principal quantum number is an integer that is the number of the electron's shell. The value is 1 or higher (never 0 or negative).

·      The angular momentum quantum number is an integer that is the value of the electron's orbital (e.g., s=0, p=1). ℓ is greater than or equal to zero and less than or equal to n-1.

·      The magnetic quantum number is the orientation of the orbital with integer values ranging from -ℓ to ℓ. So, for the p orbital, where ℓ=1, m could have values of -1, 0, 1.

·      The spin quantum number is a half-integer value that is either -1/2 (called "spin down") or 1/2 (called "spin up").

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Quantum Number Example

For the outer valence electrons of a carbon atom, the electrons are found in the 2p orbital. The four quantum numbers used to describe the electrons are n=2, ℓ=1, m=1, 0, or -1, and s=1/2 (the electrons have parallel spins).

Not Just for Electrons

While quantum numbers are commonly used to describe electrons, they may be used to describe the nucleons (protons and neutrons) of an atom or elementary particles.

Anne Marie Helmenstine, Ph.D.

·   Ph.D. in biomedical sciences from the University of Tennessee at Knoxville - Oak Ridge National Laboratory.

·   Science educator with experience teaching chemistry, biology, astronomy, and physics at the high school, college, and graduate levels.

·   ThoughtCo and About Education chemistry expert since 2001.

·   Widely-published graphic artist, responsible for printable periodic tables and other illustrations used in science.

Experience

Anne Helmenstine, Ph.D. has covered chemistry for ThoughtCo and About Education since 2001, and other sciences since 2013. She taught chemistry, biology, astronomy, and physics at the high school, college, and graduate levels. She has worked as a research scientist and also abstracting and indexing diverse scientific literature for the Department of Energy.

In addition to her work as a science writer, Dr. Helmenstine currently serves as a scientific consultant, specializing in problems requiring an interdisciplinary approach. Previously, she worked as a research scientist and college professor. 

Education

Dr. Helmenstine holds a Ph.D. in biomedical sciences from the University of Tennessee at Knoxville and a B.A. in physics and mathematics with a minor in chemistry from Hastings College. In her doctoral work, Dr. Helmenstine developed ultra-sensitive chemical detection and medical diagnostic tests.

Anne Marie Helmenstine, Ph.D.​

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https://www.thoughtco.com/definition-of-quantum-number-604629