Click initial and final electron energy levels (n=1 through n=6) to calculate photon wavelength, frequency, and energy for any hydrogen transition.
Clicking two energy levels and instantly seeing the resulting photon's exact wavelength and color turns the Rydberg formula from an equation to memorize into a relationship you can verify directly — core AP Chemistry Unit 1 content built entirely from the hydrogen atom's quantized energy levels.
Every electron transition in hydrogen, from any initial level ni down to any final level nf, releases a photon whose wavelength is given exactly by the Rydberg formula: 1/λ = R∞(1/nf² - 1/ni²), with R∞ = 1.097 × 10⁷ m⁻¹. Because hydrogen's energy levels follow En = -13.6 eV/n², larger transitions (bigger gap between ni and nf) release higher-energy, shorter-wavelength photons, while transitions between adjacent, high-n levels release lower-energy, longer-wavelength photons.
The four series are distinguished entirely by their final level: the Lyman series (nf = 1) has the largest possible energy gaps and falls entirely in the ultraviolet, invisible to the human eye. The Balmer series (nf = 2) is uniquely important because it's the only series with lines in the visible spectrum — these are the classic red, cyan, blue, and violet hydrogen emission lines visible directly in a spectroscope, historically the first spectral lines ever measured with precision. The Paschen series (nf = 3) and Brackett series (nf = 4) both fall in the infrared, invisible but detectable with appropriate instruments.
Because every transition within a series shares the same final level, series members converge as ni increases — the energy gap between consecutive transitions shrinks, and the series approaches (but never quite reaches) a series limit corresponding to complete ionization from that final level.
Photon energy, frequency, and wavelength are three ways of describing the same quantity: E = hν = hc/λ, so any transition's photon can be characterized in whichever unit a specific problem asks for, all derived from the same underlying energy-level difference.
This tool lets you click any initial and final energy level from n=1 through n=6, instantly calculates the resulting photon's wavelength, frequency, and energy, and identifies which series and spectral region it belongs to.