| n | l | Subshell | Allowed ml values | Orbitals | Max electrons | Total nodes |
|---|---|---|---|---|---|---|
| 1 | 0 | 1s | 0 | 1 | 2 | 0 |
| 2 | 1 | 2p | -1, 0, +1 | 3 | 6 | 1 |
| 3 | 2 | 3d | -2, -1, 0, +1, +2 | 5 | 10 | 2 |
| 4 | 3 | 4f | -3 to +3 | 7 | 14 | 3 |
Allowed quantum numbers:
n = 1, 2, 3, ...
l = 0, 1, 2, ..., n - 1
ml = -l, ..., 0, ..., +l
ms = +1/2 or -1/2
Orbital and electron capacity:
Orbitals in subshell = 2l + 1
Max subshell electrons = 2(2l + 1)
Orbitals in shell = n²
Max shell electrons = 2n²
Nodes:
Total nodes = n - 1
Angular nodes = l
Radial nodes = n - l - 1
Hydrogen-like estimates:
Energy = -13.605693 × Zeff² / n² eV
Bohr radius = 0.529177 × n² / Zeff Å
Photon wavelength = 1239.841984 / photon energy
- Enter the principal quantum number n.
- Enter l, then make sure it is smaller than n.
- Enter ml within the allowed negative to positive l range.
- Select the spin value as +1/2 or -1/2.
- Enter Zeff for a hydrogen-like energy estimate.
- Add electrons in the selected subshell for box filling.
- Enter initial and final n values for transition energy.
- Press calculate, then review results, graph, CSV, and PDF.
About the Calculator
Quantum numbers describe where an electron can exist. They do not draw a tiny path. They define an allowed state from a wave model. This calculator checks that state. It joins four inputs into one readable orbital report.
The principal number n sets the shell size. Larger n usually means a larger orbital and higher energy for a hydrogen like atom. The angular number l sets the subshell. It also sets the shape family. The magnetic number ml selects one orientation from that subshell. Spin ms selects the electron spin direction.
Quantum Number Rules
A valid set must follow strict rules. The value of l must start at zero. It must stay below n. The value of ml must fall between negative l and positive l. Spin must be either plus one half or minus one half. When one rule fails, the quantum state is not allowed.
Nodes and Capacity
The calculator also estimates node counts. Total nodes equal n minus one. Angular nodes equal l. Radial nodes equal n minus l minus one. These numbers help compare orbital complexity. More nodes mean more sign changes in the wave function. They also help explain shape changes across shells.
Capacity results are useful for configuration work. A subshell has two l plus one orbitals. Each orbital can hold two electrons with opposite spins. So the subshell capacity is two times that orbital count. A full shell can hold two n squared electrons.
Energy and Transitions
Use the hydrogen like energy as an estimate. It depends on effective nuclear charge and n. Real multi electron atoms need corrections. Shielding, electron repulsion, and relativistic effects can shift values. Still, the estimate gives a helpful first comparison.
The transition section compares two shell levels. If an electron drops, energy is emitted. If it rises, energy is absorbed. The wavelength is calculated from photon energy. Use it as a guide for simple spectral checks.
Best Uses
This tool is best for homework checks, teaching pages, and quick validation. Enter numbers carefully. Then compare the formulas, table, graph, and export files. The output keeps each result transparent and easy to review. Use comparisons.
1. What does this quantum number calculator do?
It checks whether n, l, ml, and ms form an allowed quantum state. It also calculates orbital notation, node counts, shell capacity, subshell capacity, energy estimates, and transition wavelength.
2. What is the principal quantum number?
The principal quantum number is n. It defines the main shell level. Higher n values usually mean larger orbitals and higher hydrogen-like energy levels.
3. Which l value matches each subshell?
l = 0 is s. l = 1 is p. l = 2 is d. l = 3 is f. Higher values use extended letter labels.
4. Why must ml stay between -l and +l?
The ml value identifies orbital orientation. A subshell with angular value l has exactly 2l + 1 orientations, running from -l through zero to +l.
5. What are radial nodes?
Radial nodes are spherical regions where the wave function changes sign. This calculator uses radial nodes = n - l - 1.
6. What are angular nodes?
Angular nodes describe directional nodal surfaces. Their count equals l. They help explain why s, p, d, and f orbitals have different shapes.
7. Is the energy value exact for all atoms?
No. The energy value is a hydrogen-like estimate. Multi-electron atoms need extra corrections for shielding, electron repulsion, and other effects.
8. Why add CSV and PDF downloads?
CSV is useful for spreadsheets and data storage. PDF is useful for homework records, reports, printed worksheets, and teaching notes.