Intermediate Topic 54 of 1102 Atomic Structure & Periodicity
Azimuthal Quantum Number
The number l, from 0 to n-1, defining the subshell and orbital shape.
Practise Atomic Structure & Periodicity All Atomic Structure & Periodicity topics
In-depth explanation of Azimuthal Quantum Number
The azimuthal quantum number, l, defines the subshell and the shape of an orbital. It takes integer values from 0 to n minus 1, with l = 0, 1, 2 and 3 corresponding to the subshells s, p, d and f. The value of l determines the orbital angular momentum, which equals the square root of l(l+1) times h / 2 pi. In many-electron atoms the energy depends on both n and l, so subshells within a shell have different energies. This is why 4s fills before 3d.
Going deeper: Azimuthal Quantum Number
Key ideas: l runs from 0 to n - 1 and defines the subshell and orbital shape: 0 = s, 1 = p, 2 = d, 3 = f. Orbital angular momentum = sqrt(l (l + 1)) x h / (2 pi). Number of orbitals in the subshell is 2 l + 1, and total angular nodes = l. Example: n = 3 has l = 0, 1, 2 (3s, 3p, 3d).
Common mistakes and connections: Students allow l = n (impossible) or write 1p, 2d, 3f, which do not exist. The angular momentum is not l x h / 2 pi. The sum n + l is used in the Madelung rule. The value of l controls the number of angular nodes and the shape.
Visualization of Azimuthal Quantum Number
The value l=1 gives the p subshell; its radial plot has no density at the nucleus, unlike s orbitals with l=0. The interactive lesson shows this as a live animation or chart.
Worked example and use case
For n = 3, l can be 0, 1 or 2, giving the 3s, 3p and 3d subshells.
Frequently asked questions about Azimuthal Quantum Number
What is Azimuthal Quantum Number?
The number l, from 0 to n-1, defining the subshell and orbital shape.
Is Azimuthal Quantum Number a beginner, intermediate or advanced topic?
Azimuthal Quantum Number is a intermediate topic in Atomic Structure & Periodicity. It builds on the vocabulary of beginner topics in this area.
What should I learn before Azimuthal Quantum Number?
Study these earlier topics in Atomic Structure & Periodicity first: Schrodinger Equation, Atomic Orbital, Principal Quantum Number.
What comes after Azimuthal Quantum Number?
The next topics in Atomic Structure & Periodicity are Magnetic Quantum Number and Spin Quantum Number.
Can I practise Azimuthal Quantum Number with quizzes?
Yes. The interactive lesson includes a self-check question on Azimuthal Quantum Number, and the Atomic Structure & Periodicity quiz draws on every topic in this area.
Where Azimuthal Quantum Number fits in Atomic Structure & Periodicity
Azimuthal Quantum Number is topic 54 of 115 in Atomic Structure & Periodicity.