Choose a mode for your quantum data. See angular momentum magnitude, parity, and allowed states. Download results to share, review, or study later easily.
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| n | l | Subshell | |L| (ħ) | Orbitals (2l+1) | ml range |
|---|---|---|---|---|---|
| 2 | 0 | s | 0 | 1 | 0 to 0 |
| 3 | 1 | p | 1.4142136 | 3 | -1 to 1 |
| 4 | 2 | d | 2.4494897 | 5 | -2 to 2 |
| 5 | 3 | f | 3.4641016 | 7 | -3 to 3 |
For orbital angular momentum, the quantum number l is a non‑negative integer. The magnitude of angular momentum is:
|L| = √(l(l+1)) · ħ
The magnetic quantum number has allowed values:
ml = −l, …, 0, …, +l (count = 2l+1)
The angular momentum quantum number l tells you how an orbital depends on angle. It separates orbital “families,” influences angular nodes, and helps label spectra. Once l is known, you can immediately count allowed orientations and predict parity behavior.
For each principal quantum number n, l must be an integer from 0 to n−1. Example: n=3 allows l=0,1,2; n=4 allows l=0,1,2,3. The “From n” mode lists every allowed l and the matching subshell letter. Validator mode confirms it quickly.
Subshell letters are shorthand for l: s→0, p→1, d→2, f→3. Higher labels continue alphabetically (skipping j), so g→4, h→5, i→6. The letter mode converts the label to l and then reports orbitals and ml range. This is useful when a table lists orbitals by letter only.
Quantum mechanics quantizes L², not L, so L² = l(l+1)ħ². Therefore the magnitude is |L| = √(l(l+1))ħ. The calculator shows |L| as a multiplier of ħ and also in J·s using ħ = 1.054571817×10⁻³⁴. Reporting both forms helps when unit systems differ across sources.
For a given l, the magnetic quantum number ml takes integer values from −l to +l. That produces 2l+1 distinct orientations and equals the number of orbitals in the subshell. Example: l=2 gives five orbitals and ml=−2,−1,0,1,2. With electron spin included, the maximum electron capacity doubles.
Orbital parity depends on l as (−1)l: even l gives even parity and odd l gives odd parity. Parity is commonly referenced in transition discussions because many electric-dipole processes require a change in l. A common classroom rule is Δl = ±1 for such transitions. Seeing parity beside l helps you sanity-check results faster.
Uppercase term letters (S, P, D, F…) represent total orbital angular momentum L in LS coupling, not a single-electron subshell l. If you know a magnitude, the tool solves l(l+1)=(|L|/ħ)² to estimate l and shows the nearest integer. Choose the correct mode to avoid mixing l and L.
It labels the orbital’s angular behavior and shape family. It is tied to the eigenvalue of L² and influences nodes, degeneracy, parity, and many spectroscopy notations used in electron configurations.
For a principal quantum number n, l can be any integer from 0 to n−1. Example: n=4 allows l=0,1,2,3. The validator mode checks this rule instantly.
Because quantum angular momentum is defined through L² eigenvalues: L²=l(l+1)ħ². Taking the square root yields |L|=√(l(l+1))ħ, which is what the calculator reports.
There are 2l+1 allowed ml values, from −l to +l. This count also equals the number of orbitals in that subshell before considering electron spin.
Lowercase letters (s, p, d, f…) map to single-electron l values. Uppercase letters (S, P, D, F…) map to total orbital angular momentum L in LS coupling. They are related ideas but not interchangeable.
Yes. Enter |L| in ħ or J·s. The tool solves l(l+1)=(|L|/ħ)² to estimate l and also shows the nearest integer, which is useful when your model requires integer l.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.