What does an atomic orbital represent?
What does an atomic orbital represent?
- Switch from 1s to 2p and rotate the cloud.
- Identify the nodal plane in the 2p state.
- Increase Z and compare size and energy.
What to measure
Units and parameter definitions are shown beside every laboratory control and live reading.
The idea underneath
A hydrogenic orbital is a stationary wavefunction in the Coulomb potential of a nucleus. The point cloud samples its probability density, not the positions of many electrons travelling on hidden paths. A 1s state is spherically symmetric. A real 2p state has two lobes of opposite amplitude sign and a nodal plane through the nucleus. Increasing nuclear charge contracts the cloud and lowers its energy by Z². The colour of each lobe encodes wavefunction sign, not positive or negative electric charge.
Eₙ=−13.6057 Z²/n² eV · ρ=|ψ|²Units and parameter definitions are shown beside every laboratory control and live reading.
Build the argument
- State the potential and boundary conditions, then solve or approximate the Schrödinger equation.
- Normalise the wavefunction so the integral of |ψ|² is one.
- Interpret measurable distributions through |ψ|²; colour indicates signed amplitude or phase only where labelled.
Worked example 1
Hydrogen 1s has E≈−13.606 eV; 2p has E≈−3.401 eV.
Worked example 2
For Z=2, all hydrogenic energy magnitudes multiply by four.
Applications
Confinement, tunnelling and orbital structure underpin semiconductor devices, scanning tunnelling microscopes and atomic spectroscopy. The scene shows probability or wave amplitude, never a hidden classical orbit.
Common misconception
A probability cloud is not a swarm of electrons. Wavefunction sign or phase is different from probability density. These are ideal single-particle models.
A further investigation
The two lobe colours represent…
Check your understanding
The two lobe colours represent…
- Wavefunction sign
- Opposite charges
- Two electrons
Explanation
Probability is nonnegative. Amplitude can have opposite signs across a node.
Model limits
One-electron Coulomb atom, real 1s and 2p_y orbitals; no electron interactions, spin or fine structure.