Hydrogen Emission Spectrum Using Bohr Model
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The Bohr atomic model was long ago superseded by modern quantum mechanics. The one system for which it does give correct results is the hydrogen atom. This Demonstration models a hydrogen atom with 10 energy levels. An electron can fall to a lower energy level or get excited to a higher energy level. If the electron falls to the second energy level (Balmer series), then it emits a colored photon; the color depends on the wavelength. A photon can also excite the electron to a higher energy level. The levels with 
are actually degenerate and depend on additional quantum numbers (
and 
).
Contributed by: Kristina Miller and Jun Tomita (June 2015)
Special thanks to the University of Illinois NetMath Program and the mathematics department at William Fremd High School.
With additional contributions by: Christopher Grattoni
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: a green photon is emitted with a wavelength of 486 nm
Snapshot 2: an ultraviolet photon is emitted with a wavelength of 92.1 nm
Snapshot 3: an infrared photon is emitted with a wavelength of 902 nm
The hydrogen emission spectrum contains four lines in the visible spectrum: 656.3 nm (red), 486.1 nm (green), 434.0 nm (blue), and 410.2 nm (violet).
Let 
and 
be the principal quantum numbers (
) of the initial and final electron orbits. The energy is 
eV. The wavelength is 
nm and the frequency is 
Hz.
References
[1] R. Nave. "Hydrogen Energy Levels." HyperPhysics. (Jun 8, 2015). hyperphysics.phy-astr.gsu.edu/hbase/hyde.html.
[2] R. Nave. "Hydrogen Emission Spectrum." HyperPhysics. (Jun 8, 2015). hyperphysics.phy-astr.gsu.edu/hbase/hyde.html.
[3] C. Honsberg and S. Bowden. "Energy of Photon." PV Education. (Jun 8, 2015) www.pveducation.org/pvcdrom/properties-of-sunlight/energy-of-photon.
Permanent Citation
Balmer Series for the Bohr Atom
D. Meliga and S. Z. Lavagnino
Rovibronic Infrared Spectrum of a Rigid Diatomic Rotor
Whitney R. Hess and Lisa M. Goss (Idaho State University)
Rate Equations for a Three-Level Model in Low-Dimensional Exciton Systems
Jessica Alfonsi
Bohr's Orbits
Enrique Zeleny
Blackbody Spectrum
Jeff Bryant
Hydrogen Orbitals
Michael Trott
Electron Waves in Bohr Atom
Ken Caviness
Hydrogen Orbital Densities
Enrique Zeleny
Spontaneous Emission in a Free-Electron Laser
Marcello Artioli, Giuseppe Dattoli, and Simonetta Pagnutti
Band Spectrum in a Periodic Potential
Michael Trott
