What is the Rydberg constant used here?

This calculator uses R∞ = 1.0973731568539 × 10⁷ m⁻¹ (Rydberg constant for infinite nuclear mass). For hydrogen-like ions, Z² scales it accordingly.

Which electron level is n1 and which is n2?

n1 is the initial (higher) energy level and n2 is the final (lower) level. The electron falls from n1 to n2, emitting a photon. For absorption, the electron jumps from n2 to n1.

What spectral series does this cover?

Lyman (n2=1, UV), Balmer (n2=2, visible/UV), Paschen (n2=3, near-IR), Brackett (n2=4, IR), and Pfund (n2=5, mid-IR). Higher series are also calculated but not named here.

Can I calculate absorption wavelengths too?

Yes. The wavelength formula is symmetric — the same wavelength is absorbed or emitted for the same pair of levels. Simply note that absorption goes from n2 up to n1.

Does this work for helium or lithium ions?

Yes, for hydrogen-like ions (one electron). Set Z=2 for He+, Z=3 for Li2+, etc. Multi-electron atoms require a different approach.

Rydberg Equation Calculator

Enter initial and final electron energy levels to calculate the photon wavelength emitted or absorbed using the Rydberg equation.

Transition Parameters

Atomic Number (Z) — 1 for hydrogen, 2 for He+, etc.

Initial Level n₁ — higher energy level (electron starts here)

Final Level n₂ — lower energy level (electron ends here)

Quick Presets

Results

Wavelength

Nanometers (nm) —

Angstroms (Å) —

Meters (m) —

Photon Energy

Electron-volts (eV) —

Joules (J) —

Frequency (THz) —

Spectral Info

Wavenumber (cm⁻¹) —

Spectral Series —

Spectral Region —

Formula: 1/λ = R_∞ × Z² × (1/n₂² − 1/n₁²) | R_∞ = 1.0974 × 10⁷ m⁻¹

Summary

The Rydberg equation relates the wavelength of emitted or absorbed light to the initial and final electron energy levels in hydrogen-like atoms. It is foundational to atomic spectroscopy and quantum mechanics, explaining the discrete spectral lines observed in hydrogen. This calculator also identifies the spectral series (Lyman, Balmer, Paschen, Brackett, or Pfund) and converts the result to common units.

How it works

Enter the atomic number Z (1 for hydrogen, 2 for He+, etc.).
Set the initial energy level n1 (higher level) and final level n2 (lower level).
The calculator applies: 1/λ = R × Z² × (1/n2² − 1/n1²).
The wavelength λ is computed and converted to nanometers, angstroms, and meters.
The spectral series and region (UV, visible, IR) are identified automatically.
The photon energy in eV and joules is also calculated from E = hc/λ.

Use cases

Solve hydrogen emission spectrum problems in chemistry and physics coursework.
Identify which spectral series a given transition belongs to.
Calculate photon energy for a specific electron transition.
Explore spectral lines for hydrogen-like ions such as He+, Li2+.
Verify textbook worked examples for the Balmer or Lyman series.
Convert wavelength between nm, Å, and meters for lab reports.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu