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# 8.4: Electron Spin

A complete specification of the state of an electron in a hydrogen atom requires five quantum numbers: n, l, m, s, and $$m_s$$. The names, symbols, and allowed values of these quantum numbers are summarized in Table $$\PageIndex{4}$$.

Table $$\PageIndex{4}$$: Summary of Quantum Numbers of an Electron in a Hydrogen Atom
NameSymbolAllowed values
Principal quantum numbern1, 2, 3, …
Angular momentuml0, 1, 2, … n – 1
Angular momentum projectionm$$0, \pm 1, \pm 2, . . . \pm l$$
Spins1/2 (electrons)
Spin projection$$m_s$$$$- 1/2, \, +1/2$$

Note that the intrinsic quantum numbers introduced in this section ($$s$$ and $$m_s$$) are valid for many particles, not just electrons. For example, quarks within an atomic nucleus are also spin-half particles. As we will see later, quantum numbers help to classify subatomic particles and enter into scientific models that attempt to explain how the universe works.

# Contributors

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).