Hydrogen Emission Spectrum Using Bohr Model

Initializing live version
Download to Desktop

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The Bohr atomic model was long ago superseded by modern quantum mechanics.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



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.


[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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.