Editing Quantum number (section)

=== Azimuthal quantum number ===
The azimuthal quantum number, also known as the ''orbital angular momentum quantum number'', describes the [[electron shell#Subshells|subshell]], and gives the magnitude of the orbital [[angular momentum]] through the relation

<math display=block>L^2 = \hbar^2 \ell(\ell + 1).</math>

In chemistry and spectroscopy, {{math|1=''{{ell}}'' = 0}} is called s orbital, {{math|1=''{{ell}}'' = 1}}, p orbital, {{math|1=''{{ell}}'' = 2}}, d orbital, and {{math|1=''{{ell}}'' = 3}}, f orbital.

The value of {{mvar|{{ell}}}} ranges from 0 to {{math|''n'' − 1}}, so the first p orbital ({{math|1=''{{ell}}'' = 1}}) appears in the second electron shell ({{math|1=''n'' = 2}}), the first d orbital ({{math|1=''{{ell}}'' = 2}}) appears in the third shell ({{math|1=''n'' = 3}}), and so on:<ref>{{cite book|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry|volume=1|first=P. W.|last=Atkins|publisher=Oxford University Press|date=1977|isbn=0-19-855129-0}}{{page needed|date=February 2019}}</ref>

<math display=block>\ell = 0, 1, 2, \ldots, n-1</math>

A quantum number beginning in {{math|1=''n'' = 3,''{{ell}}'' = 0}}, describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an [[atomic orbital]] and strongly influences [[chemical bond]]s and [[bond angle]]s. The azimuthal quantum number can also denote the number of angular nodes present in an orbital. For example, for p orbitals, {{math|1=''{{ell}}'' = 1}} and thus the amount of angular nodes in a p orbital is 1.