On this page
Your physics book says a moving electron has a wavelength, λ = h/p. That is only a guess until an experiment catches electrons doing something only waves do. In 1927 Clinton Davisson and L. H. Germer did that at Bell Telephone Laboratories in New York, without having set out to test the idea. Here is the story, the numbers for their 54-volt beam, and what to borrow from how Davisson worked.
Who was Clinton Davisson?
Davisson was born in Bloomington, Illinois, on 22 October 1881 and died in Charlottesville, Virginia, on 1 February 1958, according to his Nobel Prize facts page. He shared the 1937 Nobel Prize in Physics with George Paget Thomson "for their experimental discovery of the diffraction of electrons by crystals".
His Nobel biography shows a slow route. He entered the University of Chicago in 1902 under the influence of Robert Millikan, left the next year for financial reasons, later returned, earned a PhD at Princeton in 1911 under O. W. Richardson, and spent the summer of 1913 at the Cavendish Laboratory under J. J. Thomson, whose discovery of the electron is in your Class 12 book. In 1917 he joined Western Electric's engineering department (later Bell Telephone Laboratories) and stayed 29 years.
How did an industrial lab end up testing de Broglie?
In his Nobel lecture, "The Discovery of Electron Waves", Davisson admits the work did not begin as a test of theory. "The true story contains less of perspicacity and more of chance," he said.
The lecture gives the sequence:
1919: by accident, the team found electrons bouncing off a metal with no loss of energy (elastic scattering).
Later, again by accident: the strength of this scattering changed with the orientation of the metal's crystals.
1925: they began work on a single nickel crystal of known orientation, the year after de Broglie's thesis appeared.
Summer 1926: only after Davisson discussed the work in England with Richardson, Max Born, James Franck and others did it become a test of wave theory.
Our post on how de Broglie proposed matter waves in his PhD thesis tells the theory side. Davisson also credits Elsasser, who pointed out in 1925 that electron diffraction would prove electron waves are real.
What did the experiment show?
Electrons accelerated through a set voltage were fired at a nickel crystal face cut along its 111 planes, and a movable collector counted those bouncing off in each direction. The lecture says the search for diffraction beams began in autumn 1926 and that early in 1927 they found "first one and then twenty others in rapid succession". Nineteen of these could be used to check λ = h/p, and in every case the formula held within the accuracy of the measurements. The first report appeared in Nature on 1 April 1927 as The Scattering of Electrons by a Single Crystal of Nickel.
Why does a crystal act like a grating? The 1937 presentation speech by H. Pleijel, chair of the Nobel Committee for Physics, explains it. Each row of surface atoms sends out a scattered wave. Where the extra path from one row to the next equals a whole number of wavelengths, they add up and a strong beam comes out. Row spacing was known from X-ray studies, so a beam's angle gave the wavelength and the voltage gave the momentum. The speech says theory and experiment agreed to within 1 to 2%.
The full paper, Diffraction of Electrons by a Crystal of Nickel (Physical Review, December 1927), reports thirty sets of beams below 370 volts. Six came from gas on the surface and vanished when the crystal was cleaned by heating.
Worked example: the wavelength of a 54-volt electron
Davisson's lecture shows a strong beam at 54 volts. Find the electron's de Broglie wavelength. Use h = 6.626 × 10⁻³⁴ J s, m = 9.109 × 10⁻³¹ kg and e = 1.602 × 10⁻¹⁹ C.
Kinetic energy: K = eV = 1.602 × 10⁻¹⁹ × 54 = 8.65 × 10⁻¹⁸ J.
Momentum: p = √(2mK) = √(2 × 9.109 × 10⁻³¹ × 8.65 × 10⁻¹⁸) = √(1.576 × 10⁻⁴⁷) = 3.97 × 10⁻²⁴ kg m/s.
Wavelength: λ = h/p = (6.626 × 10⁻³⁴)/(3.97 × 10⁻²⁴) = 1.67 × 10⁻¹⁰ m = 0.167 nm.
Shortcut check: for an electron accelerated through V volts, λ ≈ 1.227/√V nm. Here √54 = 7.35, so λ = 1.227/7.35 = 0.167 nm. Davisson's graph uses the same line in ångström: λ = 12.25/√V.
That is about the size of the gaps between atoms, which is why a crystal can diffract them. The NCERT Class 12 chapter on dual nature makes the same point: an electron's de Broglie wavelength is comparable with X-ray wavelengths, while a ball's is far too small to measure.
Common mistakes:
Using V as energy. The energy is eV in joules, not 54.
Dropping the square root. p = √(2mK), not 2mK.
Mixing units. 1.227 gives nanometres; 12.27 gives ångström. Write the unit next to the constant.
Using λ = hc/E for an electron. That relation is for photons only.
Practise with our de Broglie wavelength problems with accelerating voltage.
Is the Davisson–Germer experiment in the syllabus?
The current NCERT Class 12 Physics chapter 11 (2026-27 reprint) teaches the de Broglie relation but has no section on this experiment. The JEE Main 2026 syllabus lists "Matter waves: wave nature of particle, de-Broglie relation" under Unit 17. Learn the experiment as the evidence behind the formula, and check the current year's NTA and NCERT documents.
What can a student take from Davisson's way of working?
Treat surprises as data. Twice an accident changed his direction, and twice he followed it up.
Talk to people outside your room. Conversations in England turned the work into a test of wave theory.
Check many cases. He tested the formula on nineteen beams, not one lucky peak.
Find your errors. Six sets of beams came from surface gas; heating removed them.
If picturing waves from rows of atoms is the hard part, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: work out λ for a 150-volt electron (answer: 0.100 nm), then explain in two lines why a crystal was needed to see it.
