Current leveln = 1Energy−13.60 eVTransition0.00 eVWavelength—StateGround

Electron Energy Levels

Quantized states · photons · spectra

Student Mode

Investigation

Mission: move the electron between allowed energy levels and compare their energies.

Hydrogen-like species

Initial leveln = 1

Target leveln = 2

Photon energy10.20 eV

Energy match tolerance0.15 eV

Simulation speed1.0×

Live measurements

Current energy−13.60 eV

Transition energy10.20 eV

Photon wavelength121.6 nm

Transition probability100%

Current observation

The electron occupies the ground state. Only specific energies are allowed.

Electron energy over time

electron energyphoton energy

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Interactive energy-level lesson

Ten synchronized chapters.

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Chapters

Learning objectives

Explain why electron energies are quantized.
Calculate hydrogen-like energies for levels n = 1 through 6.
Relate absorption and emission to energy differences.
Connect photon energy, frequency, wavelength, and spectral color.
Compare H, He⁺, and Li²⁺ energy spacing.

Scientific model

For a one-electron species, level energy is −13.6 × Z² ÷ n² electron volts. A photon is absorbed only when its energy matches an upward gap. A downward jump emits a photon with the same energy difference.

Try these experiments

Compare the n = 1 to n = 2 gap with n = 4 to n = 5.
Miss the absorption energy deliberately.
Emit photons ending at n = 2 and compare visible Balmer colors.
Increase nuclear charge from H to He⁺ or Li²⁺.

Applications

Energy-level transitions explain emission lamps, stellar spectra, lasers, flame tests, and astronomical element identification. Electrons do not orbit as tiny classical planets; the rings are a useful energy-level visualization.

Energy-level quiz

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