Davisson-Germer Experiment: The Day Electrons Became Waves

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Fire a beam of electrons at a nickel crystal. Watch them bounce off at various angles. Here is what happens when you actually try this: at one specific angle, the intensity spikes. Sharp peak. Not the smooth scattering you would expect from billiard-ball particles bouncing off a surface. Something else is going on.

That something is interference. Wave interference. The electrons are diffracting from the crystal lattice exactly like X-rays do. But electrons are particles, right? They have mass, charge, they leave tracks in cloud chambers. How can they interfere?

This is what Davisson and Germer stumbled onto in 1927, completely by accident. Their vacuum broke, oxidizing their nickel sample. When they cleaned it by heating, they created large single crystals without realizing it. Suddenly the smooth scattering pattern they expected became sharp diffraction peaks. They had just proved that electrons are waves. De Broglie won the Nobel Prize in 1929 for predicting this. Davisson and Thomson (who did the same experiment with faster electrons) got theirs in 1937 for proving it.

The Physics Behind the Experiment

De Broglie's Matter Wave Hypothesis

In 1924, Louis de Broglie asked what seemed like a crazy question: if light waves can act like particles (photons), why can not particles act like waves? His PhD thesis proposed exactly that. Any particle with momentum p has an associated wavelength:

lambda = h / p

where h is Planck's constant (6.626 x 10^-34 J s). The faster the particle, the shorter the wavelength. The more massive, the shorter still.

For an electron accelerated through potential V, the kinetic energy is:

E = eV = p^2 / (2m_e)

Solving for momentum and substituting (do the algebra, it is worth seeing):

lambda = h / sqrt(2 m_e e V)

For V = 54 V (the original experiment), this gives lambda approximately equal to 0.167 nm. That is about the spacing between atoms in a crystal. If electrons are waves, crystals should diffract them like X-rays.

Bragg's Law for Diffraction

When waves scatter from a regular array of atoms, they interfere constructively only at specific angles. The condition is simple geometry: the path difference between waves from adjacent planes must equal an integer number of wavelengths.

n lambda = 2d sin(theta)

Here d is the spacing between crystal planes, theta is the scattering angle, and n is the order of diffraction (1, 2, 3...).

The Original Experiment

Davisson and Germer used a nickel crystal with lattice spacing d = 0.091 nm. With 54 V electrons (lambda = 0.167 nm), Bragg's law predicts a first-order peak at:

theta = arcsin(lambda / 2d) = arcsin(0.167 / 0.182) = 66.5 deg

But here is the puzzle: they observed the peak at 50 degrees, not 66.5 degrees. Wrong by 16 degrees. Did they disprove de Broglie?

No. The discrepancy arises because electrons refract when entering the crystal. The inner potential of nickel accelerates them slightly, shortening their wavelength inside the material. Include this correction and the agreement is excellent. Actually, this made the result more convincing, not less. They understood the physics deeply enough to explain the discrepancy.

How to Use This Simulation

Here's what happens when you actually try this: set the voltage to 54 V (exactly what Davisson and Germer used) and watch the polar plot. A sharp peak appears at around 50 degrees. That peak is the smoking gun for electron wave behavior.

Main Controls

Historic Presets

Electron Gun Parameters

The derived values update automatically:

• Kinetic Energy (in eV): equals the accelerating voltage
• de Broglie Wavelength (in nm): lambda = h / sqrt(2 m_e e V)

Crystal Parameters

If you could slow this down enough to watch, you'd see that the detector only registers a strong signal when Bragg's law is satisfied. Move the detector to the wrong angle and the electrons scatter randomly. Put it at the Bragg angle and you get constructive interference.

Bragg's Law Verification Panel

The simulation continuously checks Bragg's law: n lambda = 2d sin(theta)

Visualization Panels

Results Strip

Bottom Tabs

Keyboard Shortcuts

Tips for Exploration

1. Start with the Original 1927 preset: This recreates history. Watch the polar plot peak appear at 50 degrees.

2. Verify Bragg's law manually: At 54 V, lambda is about 0.167 nm. With d = 0.091 nm, calculate where the peak should be. Does it match?

3. Increase voltage and watch the peak shift: Higher voltage means shorter wavelength. The diffraction angle decreases. This is the inverse relationship between wavelength and diffraction angle.

4. Look for second-order peaks: At higher voltages, you can sometimes see n=2 diffraction. These confirm that the pattern really is wave interference, not some artifact.

5. Use the Export Report button: Generate a professional summary of your experiment with all parameters and Bragg verification included.

Exploration Activities

Activity 1: Reproduce the Original Result

Objective: Step into Davisson and Germer's shoes. Recreate 1927.

Steps:

1. Set voltage to 54 V (exactly what they used)
2. Set lattice spacing to 0.091 nm (nickel)
3. Observe the polar plot. Where does the peak appear?
4. Find the peak intensity angle
5. Compare with Bragg's law prediction
6. Note how the Bragg equation verification shows "Match!" near 50 degrees

They saw this pattern and realized they had made physics history.

Activity 2: Explore Voltage Dependence

Objective: Higher voltage means faster electrons means shorter wavelength. See it happen.

Steps:

1. Start at 54 V and note the peak angle
2. Increase voltage to 100 V and watch the peak shift
3. Continue to 150 V and 200 V
4. Record wavelength and peak angle at each voltage
5. Verify that higher voltage gives smaller diffraction angles
6. Plot lambda vs V. You should see the inverse square root relationship: lambda proportional to 1/sqrt(V)

Activity 3: Second-Order Diffraction

Objective: Find the higher-order peaks that Bragg's law predicts.

Steps:

1. Set voltage to approximately 150 V
2. Look for peaks at larger angles than the first-order peak
3. These correspond to n = 2 in Bragg's law
4. Calculate expected angle using n lambda = 2d sin(theta)
5. Compare with simulation results

Multiple orders are the signature of real diffraction. Single peaks could be flukes. Multiple peaks at predicted angles are not.

Activity 4: Bragg's Law Verification

Objective: Check Bragg's law quantitatively. Physics lives and dies by the numbers.

Steps:

1. For several voltage settings, record the peak angle
2. Calculate n lambda for each case
3. Calculate 2d sin(theta) for each case
4. Create a table comparing both sides of Bragg's equation
5. Quantify the agreement (should be within a few percent)

If the numbers match, you have verified the de Broglie wavelength formula.

Real-World Applications

Electron Microscopy

The wave nature of electrons enables electron microscopes to achieve resolution far beyond optical microscopes. Because electron wavelengths (0.01-0.1 nm at typical accelerating voltages) are much shorter than visible light (400-700 nm), electron microscopes can resolve individual atoms.

Transmission electron microscopes (TEM) pass electrons through thin samples, while scanning electron microscopes (SEM) scan a focused beam across surfaces. Both techniques are essential in materials science, biology, and nanotechnology.

Low-Energy Electron Diffraction (LEED)

LEED uses low-energy electrons (20-500 eV) to probe surface structure. The electrons penetrate only the first few atomic layers, making LEED extremely sensitive to surface reconstruction, adsorbed molecules, and thin films. It is a standard tool in surface science laboratories.

Electron Crystallography

For samples too small or delicate for X-ray crystallography, electron diffraction provides an alternative. Recent advances in cryo-electron microscopy (cryo-EM) have revolutionized structural biology, enabling atomic-resolution structures of proteins and viruses without growing crystals.

Quantum Mechanics Foundation

Beyond applications, the Davisson-Germer experiment fundamentally changed our understanding of nature. It showed that wave-particle duality is not just a quirk of light but a universal property of all matter. This realization was essential for developing quantum mechanics and modern physics.

Physical Constants Reference

Challenge Questions

Level 1: Conceptual

1. Why do electrons diffract from crystals but not from smooth surfaces?

2. If you double the accelerating voltage, what happens to the electron wavelength?

Level 2: Analytical

1. Calculate the de Broglie wavelength for electrons accelerated through 100 V. Compare with the wavelength of visible light.

2. For a crystal with d = 0.2 nm, at what electron energy would you observe first-order diffraction at 45 degrees?

Level 3: Advanced

1. The original experiment found the peak at 50 degrees, not the 66.5 degrees predicted by simple Bragg's law. The discrepancy arises from electron refraction at the crystal surface. If the inner potential is 12 V, show that this accounts for the difference.

2. Thermal neutrons (E approximately equal to kT at room temperature) also diffract from crystals. Calculate their wavelength and compare with electrons at 54 V. Why are both useful for studying crystal structure?

3. In LEED, why are low-energy electrons (20-500 eV) used rather than higher energies like in TEM?

Common Misconceptions

These errors persist even among people who should know better. Avoid them.

Frequently Asked Questions

Why was the vacuum break actually helpful to the experiment?

Happy accident. The vacuum break oxidized the nickel surface. When Davisson and Germer cleaned it by heating (annealing at high temperature), the polycrystalline sample recrystallized into large single crystals [1]. Polycrystals give smeared patterns. Single crystals give sharp peaks. The vacuum failure made the experiment work.

Why did de Broglie propose matter waves?

Einstein showed that light waves have particle properties (photons). De Broglie asked the obvious question: if waves can act like particles, why can not particles act like waves? His thesis advisor was skeptical. Einstein endorsed the idea enthusiastically [2]. Three years later, Davisson and Germer proved Einstein right.

How accurate was the experimental confirmation?

Within about 1%. When corrections for the inner potential of the crystal are included, the agreement is even better [3]. This level of precision distinguished the result from a fluke. You can not get 1% agreement from a wrong theory.

Could larger objects show wave behavior?

In principle yes, but the wavelengths become absurdly small. A baseball moving at 40 m/s has lambda approximately 10^-34 m [4]. That is 10^-19 times smaller than a proton. You would need a diffraction grating with atomic nuclei spaced closer than nucleon diameters. Never going to happen. Only particles with very small mass and low speed have observable wavelengths.

What is the "inner potential" mentioned in advanced treatments?

When electrons enter a crystal, they see an average attractive potential from all the positive ion cores. This accelerates them by about 10-20 eV, which shortens their wavelength inside the material [5]. The effect shifts diffraction angles from the simple Bragg prediction. Davisson and Germer figured this out, which made their result more convincing, not less.

References

1. Davisson, C. and Germer, L.H. "Diffraction of Electrons by a Crystal of Nickel," Physical Review, 30(6), 705-740, 1927.

2. de Broglie, L. "Recherches sur la theorie des quanta," PhD thesis, University of Paris, 1924. Available at: https://www.academie-sciences.fr/pdf/dossiers/Broglie/Broglie_pdf/CR1923_p507.pdf

3. MIT OpenCourseWare 8.04: Quantum Physics I. Lecture notes on matter waves. Available at: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/

4. NIST: Fundamental Physical Constants. Available at: https://physics.nist.gov/cuu/Constants/

5. Kittel, Charles. "Introduction to Solid State Physics," 8th Edition, Wiley, 2004. Chapter 2: Wave Diffraction.

6. The Nobel Prize: Clinton Davisson Nobel Lecture 1937. Available at: https://www.nobelprize.org/prizes/physics/1937/davisson/lecture/

7. HyperPhysics: Davisson-Germer Experiment. Georgia State University. Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger.html

8. APS Physics: "Electron Diffraction at 90." Available at: https://physics.aps.org/articles/v10/21

9. The Feynman Lectures on Physics: Quantum Behavior. Volume III, Chapter 1. Available at: https://www.feynmanlectures.caltech.edu/III_01.html

10. OpenStax University Physics: "The Wave Nature of Matter." Available at: https://openstax.org/books/university-physics-volume-3/pages/6-6-the-wave-nature-of-matter

About the Data

Physical constants used in this simulation are from NIST CODATA 2022 values:

• Planck constant: h = 6.62607015 x 10^-34 J s (exact by definition since 2019)
• Electron mass: m_e = 9.1093837015 x 10^-31 kg
• Elementary charge: e = 1.602176634 x 10^-19 C (exact by definition since 2019)

The nickel lattice spacing d = 0.091 nm corresponds to the {111} crystal planes of face-centered cubic nickel with lattice constant a = 0.352 nm, where d = a / sqrt(3).

How to Cite

Simulations4All Team. "Davisson-Germer Electron Diffraction Simulator: Interactive Matter Wave Demonstration." Simulations4All, 2025. https://simulations4all.com/simulations/davisson-germer-electron-diffraction

For academic use:

@misc{simulations4all_davisson_germer, title = {Davisson-Germer Electron Diffraction Simulator}, author = {Simulations4All Team}, year = {2025}, url = {https://simulations4all.com/simulations/davisson-germer-electron-diffraction} }

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