Science, Tech, Math › Science Quantum Number Definition Share Flipboard Email Print Lawrence Lawry/Getty Images Science Chemistry Chemical Laws Basics Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Anne Marie Helmenstine, Ph.D. Chemistry Expert Ph.D., Biomedical Sciences, University of Tennessee at Knoxville B.A., Physics and Mathematics, Hastings College Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels. our editorial process Facebook Facebook Twitter Twitter Anne Marie Helmenstine, Ph.D. Updated December 12, 2019 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 levelℓ - azimuthal or angular momentum quantum number: describes the subshellmℓ or m - magnetic quantum number: describes the orbital of the subshellms or s - spin quantum number: describes the spin 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 (for example, 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"). 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.