The three relationships
Eₙ = −13.6 / n² eVHydrogen bound-state energy.
Ephoton = |Ef − Ei| = hν = hc/λEnergy difference determines the photon.
λ (nm) = 1239.84 / Ephoton (eV)Larger gaps give shorter wavelengths.
n: principal quantum number · h: Planck constant · ν: frequency · c: speed of light · λ: wavelength. One electron volt (eV) = 1.602 × 10⁻¹⁹ joules.
Read the visual model
The tube, power supply, optical source, and spectrometer represent laboratory equipment. The magnified atom and energy ladder are explanatory views, not objects inside a real glass instrument.
One teal electron marker appears in both representations. Rings show energy states, not literal orbits. The halo is illustrative, not a calculated quantum orbital. Slow transitions and photon travel are teaching animations, not real time or real distances.
We show n = 1 to 6, omit fine structure and angular-momentum selection rules, and use a 0.015 eV matching tolerance for usability. Real line widths, transition probabilities, lifetimes, and detector efficiency are not simulated. A matching event is demonstrated deterministically, not assigned a real absorption probability.
The energy ladder uses a linear energy scale, with an enlarged upper-level inset for readability. Ring spacing is schematic. UV and IR markers are dashed because these wavelengths are invisible.
Model reference: NIST hydrogen energy levels and spectral lines; the rounded −13.6 eV approximation gives wavelengths close to tabulated values, not precision spectroscopy.