Rydberg lines for Lyman/Balmer/Paschen/Brackett/Pfund: vacuum wavelengths, photon energies, named lines with Balmer colors, series limit.
Execution
Run this tool
Fill in the form, run the tool, and review the result in one place.
Samples
Examples that match this tool
Related
Continue with connected tools and hubs
Tool usage guide
Learn when to use this tool, what it supports, and how real users apply it.
Key facts
Category
Science & Education
Input types
select, number
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Hydrogen Spectrum Series Calculator computes atomic hydrogen spectral line wavelengths and photon energies using the Rydberg formula. It provides vacuum wavelengths, electronvolt values, standard line names (such as Hα, Hβ, Lyman α), Balmer color designations, and series convergence limits across the Lyman, Balmer, Paschen, Brackett, and Pfund series.
When to use
Determining exact vacuum wavelengths and photon energies for specific hydrogen electron transitions.
Analyzing visible emission lines or interstellar absorption features in physics and astronomy coursework.
Calculating the series convergence limit and ionization energies for hydrogen spectral series.
How it works
1Select the target spectral series (Lyman n=1, Balmer n=2, Paschen n=3, Brackett n=4, or Pfund n=5).
2Set the highest upper principle quantum number (maxUpper n) between 2 and 40.
3The tool applies the Rydberg formula 1/λ = R∞(1/m² − 1/n²) to calculate transition wavelengths, energies in eV, line labels, and the series limit.
Use cases
Physics students verifying theoretical spectral wavelengths against spectroscopic laboratory measurements.
Astronomy researchers identifying hydrogen absorption and emission features in stellar and nebular spectra.
Educators generating reference data tables for atomic physics lectures on the Bohr model and Rydberg transitions.
Examples
1. Visible Balmer Lines for Spectroscopy Lab
Undergraduate Physics Student
Background
Conducting a laboratory experiment measuring emission lines from a hydrogen discharge tube using a diffraction grating spectrometer.
Problem
Needs precise theoretical vacuum wavelengths and photon energies for the visible Balmer series lines up to n=10 to compare with lab readings.
How to use
Select 'Balmer (n → 2, visible + UV)' from the series dropdown and set 'Highest upper level n' to 10.
Outcome
Generates transition lines from 3→2 (Hα at 656.112 nm) down to 10→2 (379.790 nm) and the series limit at 364.507 nm.
2. Lyman Series UV Calculations for Astronomy
Astrophysics Teaching Assistant
Background
Preparing reference solutions for an astrophysics problem set on interstellar Lyman-alpha absorption.
Problem
Requires exact photon energies in eV and vacuum wavelengths for the Lyman series up to n=6.
How to use
Select 'Lyman (n → 1, ultraviolet)' as the series and specify 6 as the highest upper level n.
Outcome
FAQ
Which constant is used for the Rydberg calculation?
The calculator uses the Rydberg constant for infinite nuclear mass (R∞ ≈ 1.09737 × 10⁷ m⁻¹) to compute vacuum wavelengths.
Which hydrogen series contains visible light?
The Balmer series (transitions ending at n=2) contains visible lines: Hα (red), Hβ (blue-green), Hγ (violet-blue), and Hδ (violet).
What is the series limit?
The series limit is the shortest wavelength in a series, representing an electron transition from n = ∞ to the lower energy level m.
What is the maximum upper energy level supported?
You can calculate transitions up to a maximum upper principal quantum number (n) of 40.
Are calculated wavelengths measured in air or vacuum?
All outputs represent vacuum wavelengths in nanometers (nm) along with corresponding photon energy in electronvolts (eV).