Atomic Orbitals Lab
Visualize hydrogen atom wave functions in real time. Select quantum numbers to see orbital shapes as 2D density plots, radial probability distributions, and energy level diagrams. Explore how n, ℓ, and m determine the size, shape, and orientation of electron orbitals.
Guided Experiment: Exploring Quantum Numbers
How do the quantum numbers n, ℓ, and m affect the shape, size, and energy of hydrogen orbitals? What patterns do you expect for node counts?
Write your hypothesis in the Lab Report panel, then click Next.
Controls
Orbital Properties
Data Table
(0 rows)| # | n | ℓ | m | Orbital | Energy (eV) | Radial Nodes | Angular Nodes | Total Nodes |
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Reference Guide
Quantum Numbers
Three quantum numbers describe each orbital in the hydrogen atom.
The principal number n sets the energy and overall size. The angular momentum number ℓ sets the orbital shape (s, p, d, f). The magnetic number m sets the orientation.
Hydrogen Wave Function
The wave function separates into radial and angular parts.
The probability density |ψ|² gives the likelihood of finding the electron at each point. Bright regions in the heatmap show where the electron is most likely found.
Radial Probability Distribution
The radial probability gives the likelihood of finding the electron at distance r from the nucleus, summed over all angles.
Radial nodes (where P(r) = 0) are points where the radial wave function changes sign. The number of radial nodes is n − ℓ − 1.
Energy Levels and Spectral Lines
In hydrogen, the energy depends only on the principal quantum number n. All subshells with the same n have the same energy (they are degenerate).
The ground state (n = 1) has E = −13.6 eV. As n increases, levels get closer together, converging to 0 eV at ionization.