s Orbital Simulation

Highlighted visual caption

Basic idea: an s orbital is a spherical region showing where an electron may be detected around the nucleus.

Live changes

Orbital 1s

Quantum set 1, 0, 0

Energy −13.60 eV

Radial nodes 0

Measurements 0

Probe shell 0.0%

Teacher modeStudent · guided

Learning path · basic to advanced

Learn s orbitals in the right order

1 · BasicsMeaning, nucleus, and spherical shape

2 · BuildCompare 1s, 2s, and 3s

3 · AdvancedNodes, probability, and equations

Start here · one idea at a time

See the spherical layers first

1s: one spherical probability cloud, with no radial gap.

How to read the picture

Coloured volume shows a three-dimensional probability region.
Moving dots are probability samples—not an electron path.
Clear spherical gaps are radial nodes where probability is zero.

Predict · run · explain

Prepare and inspect

Simulation speed 1×

Hydrogen s orbital

3D viewing scale

Cloud detail 900 points

Cloud visibility 65%

Open radial cutawayShow spherical nodes

positive Ψ regionnegative Ψ regionmeasurements

Use Fit each orbital first. Drag to rotate the scanner ring; the spherical cloud itself looks unchanged from every direction.

Measure probability

Each marker is a separate, identically prepared atom—not a trail from one electron.

Radial probe 2.00 a₀

Live equations

Inspect the apparatus

Tap the nucleus, cloud, radial node, scanner shell, detector panel, or graph for its role.

Camera

Zoom 1×

Subtle detector sound

Basics first

What is an s orbital?

An orbital is not a path. It is a probability description for an electron.
The letter s means spherical shape: the probability pattern is the same in every direction around the nucleus.
1s is the simplest s orbital. It has one continuous spherical region and no radial node.
The first number is n. Moving from 1s to 2s to 3s increases energy, size, and the number of radial nodes.

Learning objectives

Explain why 1s, 2s, and 3s are spherically symmetric.
Predict s-orbital radial nodes using n − 1.
Distinguish point probability density from radial shell probability.
Connect wavefunction sign changes to spherical nodal gaps.
Use repeated position measurements as evidence for a probability distribution.

Advanced after the basics

Equations with meaning

Ψₙ₀₀(r, θ, φ) = Rₙ₀(r)Y₀₀For s orbitals the angular factor is constant, producing spherical symmetry.
Probability density = |Ψ|²Likelihood per unit volume near a point.
Radial probability = r²|Rₙ₀(r)|²Probability per radial interval after every direction is combined.
s-orbital radial nodes = n − 1Because ℓ = 0 for every s orbital.
Eₙ = −13.6 eV / n²Hydrogenic energy for nuclear charge Z = 1.

For s orbitals: n = 1, 2, 3…; ℓ = 0; mℓ = 0. One Bohr radius a₀ is approximately 0.0529 nm.

Suggested experiments

Compare 1s, 2s, and 3s at one scale and identify what remains spherical.
Predict the node count before preparing each orbital.
Open the cutaway and move the radial probe across the 2s node.
Compare dot density near the nucleus with the peak of the radial graph.
Collect 80 positions for 3s and look for missing counts at both nodes.
Compare the three hydrogen energies and explain the trend with n.

Model boundaries

This is a one-electron, nonrelativistic hydrogen model. It is not a planetary atom, an electron path, or an exact many-electron atom. Only 1s, 2s, and 3s are included so their radial structure can be studied carefully.

The glass tomography chamber, scanner shell, source and detector modules, and radial display are illustrative teaching apparatus—not a calibrated instrument or direct photograph. Cloud dots and green markers are Monte Carlo samples from analytic hydrogenic probability densities. Continuous tails extend beyond the finite view.

Fine structure, Lamb shift, spin, time-dependent transitions, relativistic corrections, detector dynamics, shielding, penetration, and electron-electron repulsion are excluded. One spatial s orbital may hold at most two opposite-spin electrons, but occupancy is not simulated.