a number expressing the magnitude of a physical quantity in units appropriate to a given quantum mechanical system

# quantum number

quantum numberWebster's New World College Dictionary, Fifth Edition Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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Quantum number. (n.d.). In

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noun

Any of a set of real numbers assigned to a physical system that individually characterize the properties and collectively specify the state of a particle or of the system.

THE AMERICAN HERITAGE® DICTIONARY OF THE ENGLISH LANGUAGE, FIFTH EDITION by the Editors of the American Heritage Dictionaries. Copyright © 2016, 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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"Quantum number."

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Quantum number. (n.d.). In

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Any of a set of numbers that together fully determine the state of a quantum mechanical system by quantifying its individual properties. For example, four quantum numbers are used to specify the quantum state of an electron orbiting the nucleus of an atom: one characterizes its basic orbital energy level (principal or first quantum number),
one the shape of its orbit (its azimuthal, orbital or second quantum number),
one the orientation of its orbit relative to other orbits (magnetic or third quantum number),
and one its spin (spin or fourth quantum number).

**Quantum numbers are used in quantum mechanics to describe the possible states of a physical system. Because many physical properties are**

*A Closer Look**quantized,*taking on only discrete, distinct values, quantum numbers are generally integers or simple fractions, rather than continuous ranges. One of the great successes of quantum mechanics is its account of the structure of electron orbits around atomic nuclei, and the state of an electron in this particular system can be described using four quantum numbers. These are the principal or first quantum number, the orbital, azimuthal, or second quantum number, the magnetic quantum number, and the spin or spin magnetic quantum number. The

*principal quantum number,*designated

*n,*characterizes the basic energy level for the electron, and indicates in which shell the electron is located. It has integer values starting at 1; the higher the number, the farther the electron is from the atom's nucleus. The principal quantum numbers correspond to the traditional orbital shell designations K, L, M, and so on, used in chemistry. The

*orbital quantum number,*designated

*l,*characterizes the electron's angular momentum and determines the shape of it orbit. Its possible values for a given electron depend on the value of that electron's principal quantum numbers, ranging from 0 to

*n*−1. Because of these different possibilities, shells (other than the first shell) include

*subshells.*These are traditionally designated

*s*(where

*l*=0),

*p (where*

*l*=1),

*d*(where

*l*=2), and

*f*(where

*l*=3). The

*magnetic quantum number,*designated

*m*or

*ml,*takes on integer values between −l and +l, and indicates the orientation of the electron's orbit within the subshell. For example, there are three orbitals in the

*p*subshell, designated as

*p*,

_{x}*p*, and

_{y}*p*. Finally, the

_{z}*spin quantum number,*designated

*ms,*characterizes the spin direction of the electron. It can have values of +

^{1}/

_{2}or −

^{1}/

_{2}. Electrons are fermions, meaning that no two electrons can be in the same quantum state (due to the

*Pauli exclusion principle*); therefore, each electron in an atom is uniquely characterized by a set of these four quantum numbers. In fact, the chemical properties of atoms depend almost entirely on the quantum numbers associated with their electrons. Other quantum numbers are used to describe other physical systems, such as the shell structure of the atomic nucleus.

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"Quantum number."

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Quantum number. (n.d.). In

*YourDictionary*. Retrieved from https://www.yourdictionary.com/quantum-numberEnglish Wiktionary. Available under CC-BY-SA license.

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*YourDictionary*. Retrieved from https://www.yourdictionary.com/quantum-number