Azimuthal Quantum Number Definition

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The azimuthal quantum number, ℓ, is the quantum number associated with the angular momentum of an atomic electron. It is also known as the angular momentum quantum number or the second quantum number. The angular momentum quantum number determines the shape of the electron's orbital. Arnold Sommerfeld proposed the azimuthal quantum number, based on the Bohr model of the atom.

Azumuthal Quantum Numbers

The azimuthal quantum numbers are:

  • Intrinsic angular momentum quantum number (spin quantum number)
  • Magnetic quantum number
  • Orbital angular momentum quantum numbers
  • Total angular momentum quantum numbers


A p orbital is associated with an azimuthal quantum number equal to 1.


  • Eisberg, Robert (1974). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. New York: John Wiley & Sons Inc. pp. 114–117. ISBN 978-0-471-23464-7.
  • Lindsay, R.B. (1927). "Note on "pendulum" orbits in atomic models." Proc. Natl. Acad. Sci. 13: 413–419. doi:10.1073/pnas.13.6.413
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Helmenstine, Anne Marie, Ph.D. "Azimuthal Quantum Number Definition." ThoughtCo, Aug. 29, 2020, Helmenstine, Anne Marie, Ph.D. (2020, August 29). Azimuthal Quantum Number Definition. Retrieved from Helmenstine, Anne Marie, Ph.D. "Azimuthal Quantum Number Definition." ThoughtCo. (accessed June 6, 2023).