Orbital Inputs and Quantum Validation
Interactive Three-Dimensional Orbital Viewer
Drag to rotate. Scroll to zoom. Right-drag to pan. Phase colours show the sign of the real wavefunction.
Graphs, Cross-Sections, and Energy View
Orbital Comparison
| Property | First orbital | Second orbital |
|---|
Comparison values use the hydrogen-like or effective-charge model selected above.
Formula Used
How to Use
- Select a preset or enter n, l, and m.
- Choose spin, nuclear charge, and effective charge.
- Enter coordinates for pointwise wavefunction evaluation.
- Set the radial interval for integrated probability.
- Add a second orbital for comparison.
- Press Calculate orbital to refresh server-side results.
- Adjust viewer controls without reloading the page.
- Export results, charts, or a viewer screenshot.
Example Data
| Species | Orbital | n | l | m | Zeff | Expected shape |
|---|---|---|---|---|---|---|
| H | 1s | 1 | 0 | 0 | 1 | Spherical |
| H | 2pz | 2 | 1 | 0 | 1 | Two lobes |
| H | 3dz² | 3 | 2 | 0 | 1 | Two lobes and torus |
| He⁺ | 2s | 2 | 0 | 0 | 2 | Concentric radial regions |
| Li²⁺ | 3p | 3 | 1 | 0 | 3 | Two lobes with radial node |
Frequently Asked Questions
What is an atomic orbital?
An orbital is a quantum wavefunction for an electron. Its squared magnitude gives a spatial probability density. It is not a fixed planetary path.
What do n, l, and m represent?
The number n controls shell energy and scale. The number l controls subshell shape and angular nodes. The number m controls spatial orientation.
Why are two phase colours shown?
The colours represent positive and negative wavefunction signs. They do not represent positive and negative electric charge. Phase matters during orbital overlap.
Are these calculations exact for every atom?
They are exact for one-electron hydrogen-like species. Multi-electron atoms require approximations or numerical quantum chemistry. Effective charge offers a simplified estimate.
What is a radial node?
A radial node is a spherical region where probability vanishes. Its count equals n minus l minus one. Higher shells can contain several radial nodes.
What is an angular node?
An angular node comes from the spherical harmonic. Its count equals l. It may appear as planes or cones.
Why can an orbital have several orientations?
Each allowed m value represents an angular solution. Real orbital combinations produce familiar labelled orientations. External fields can alter their energies.
What does the probability interval mean?
It integrates radial probability between two radii. Angular probability is already normalised in that calculation. Results approach one at sufficiently large radius.
How is the electron configuration generated?
The calculator uses the common Aufbau filling sequence. It estimates unpaired electrons using Hund’s rule. Some real atoms have known configuration exceptions.
Can this viewer show hybrid orbitals?
The hybrid selector reports standard ideal bond angles. The main three-dimensional surface remains an atomic eigenfunction. Hybrid combinations are marked as educational extensions.
Scientific Scope and Limitations
This calculator evaluates normalised hydrogenic radial functions and real spherical harmonics through f orbitals. Effective nuclear charge can approximate screening in multi-electron atoms. Accurate many-electron orbitals require Hartree–Fock, density-functional, or correlated methods.
Displayed surfaces are visual boundaries rather than hard electron edges. The electron can be found beyond every chosen surface. Rendering resolution changes appearance, not underlying quantum numbers.