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Quantum Number Validity and Orbital Capacity — result sheet
Check a set of electron quantum numbers and calculate its shell, subshell, orbital, and electron capacities.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: 0 ≤ ℓ ≤ n−1; −ℓ ≤ mℓ ≤ ℓ; mₛ = ±½; shell capacity = 2n²; subshell capacity = 2(2ℓ+1).
The four quantum numbers describe an electron's principal shell, subshell shape, orbital orientation, and spin. The handler first checks the allowed integer ranges, then reports the number of orbitals in the selected subshell, its maximum electron capacity, and the maximum capacity of the complete shell.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Principal quantum number n — minimum 1; maximum 50
- Angular-momentum quantum number ℓ — minimum 0; maximum 49
- Magnetic quantum number mℓ — minimum -49; maximum 49
- Spin quantum number mₛ — 2 choices
Worked example
| Input | Value |
|---|---|
| Principal quantum number n | 3 |
| Angular-momentum quantum number ℓ | 1 |
| Magnetic quantum number mℓ | 0 |
| Spin quantum number mₛ | 0.5 |
Valid 3p state; the subshell has 3 orbitals and capacity for 6 electrons, while shell n=3 holds 18.
Assumptions and limits
- The calculator uses the conventional single-electron quantum-number rules taught for atomic orbitals.
- The capacity values count possible states under the Pauli exclusion principle and do not solve an atom's full many-electron energy ordering.
- The orbital letter label follows the standard sequence s, p, d, f, g, h and onward for the selected ℓ value.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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