Explain Davisson-Germer experiment and its significance

Question

Describe the Davisson-Germer experiment. What did it demonstrate? Why is it significant in modern physics?

Solution — Step by Step

In 1924, Louis de Broglie proposed that matter (not just light) has wave-like properties. Every particle with momentum $p$ has an associated wavelength:

\lambda = \frac{h}{p} = \frac{h}{mv}

For electrons: at typical laboratory energies, de Broglie wavelengths are on the order of 0.1–1 nm — the same scale as atomic spacings in crystals. This suggested that electrons should show diffraction if directed at a crystal lattice, just as X-rays do.

The Davisson-Germer experiment tested and confirmed this prediction.

Clinton Davisson and Lester Germer (Bell Labs, USA, 1927) set up the following:

An electron gun produced a beam of electrons accelerated through a known voltage $V$ .
The electrons hit a nickel crystal target. When nickel was accidentally annealed (recrystallised into a single large crystal during an accident in the lab in 1925), they found a startling change in the electron scattering pattern.
A detector could be moved to measure the number of electrons scattered at different angles $\phi$ from the incident beam.

Key parameters:

Accelerating voltage: varied between 40–68 V
Detector angle: measured as angle from the incident beam direction

At an accelerating voltage of 54 V and a scattering angle of 50° from the incident beam, a sharp maximum (strong peak) in the scattered electron intensity was observed.

This is exactly what you would expect from Bragg’s law of diffraction if electrons were waves diffracting off the crystal planes of nickel:

n\lambda = 2d\sin\theta

For nickel, the interplanar spacing $d = 0.091$ nm. Using Bragg’s law with $n = 1$ and the observed diffraction angle, the predicted wavelength is:

\lambda_{experiment} \approx 0.165 \text{ nm}

Now, the de Broglie wavelength for electrons accelerated through 54 V:

\lambda_{deBroglie} = \frac{h}{\sqrt{2meV}} = \frac{6.626 \times 10^{-34}}{\sqrt{2 \times 9.11 \times 10^{-31} \times 1.6 \times 10^{-19} \times 54}}

\lambda_{deBroglie} \approx 0.167 \text{ nm}

The experimental and theoretical values agree within 1%! This confirmed de Broglie’s hypothesis.

The Davisson-Germer experiment provided the first direct experimental confirmation of de Broglie’s matter-wave hypothesis. It demonstrated conclusively that:

Electrons are not just particles — they exhibit wave-like behaviour (diffraction and interference), just as light does.
Wave-particle duality is real, not just a mathematical abstraction.
Quantum mechanics is correct — the de Broglie relation $\lambda = h/p$ accurately predicts experimental results.

The experiment earned Davisson the Nobel Prize in Physics (1937), shared with G.P. Thomson (who independently demonstrated electron diffraction using thin metal films).

Wave-particle duality of electrons has led to:

Electron microscopy: Electrons have much smaller wavelengths than visible light → can image objects at atomic resolution (nanometre scale). Modern electron microscopes can image individual atoms.
Electron diffraction: Used to determine crystal structures (like X-ray crystallography but for surfaces and thin films).
Quantum mechanics foundations: Led to the development of the Schrödinger equation, quantum tunnelling, and all of modern solid-state physics and electronics.

The transistor (basis of all computers) and semiconductor physics rest on quantum mechanical principles first validated by this experiment.

Why This Works

The crystal acts as a diffraction grating for electron waves. The regular atomic spacing in the nickel crystal is comparable to the de Broglie wavelength of the electrons. When waves encounter a periodic structure with spacing comparable to their wavelength, they diffract — constructive interference produces the sharp peaks seen in the experiment.

This is the same physics as X-ray diffraction (Bragg’s law, 1913) — but with electrons instead of photons. The fact that both particles of light (photons) and particles of matter (electrons) show identical diffraction behaviour validates wave-particle duality as a fundamental property of quantum mechanics.

Alternative Method — Calculating de Broglie Wavelength

For any electron accelerated through voltage $V$ :

The electron gains kinetic energy $eV$ :

\frac{1}{2}mv^2 = eV \Rightarrow mv = \sqrt{2meV}

de Broglie wavelength:

\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2meV}} = \frac{1.226}{\sqrt{V}} \text{ nm}

At $V = 54$ V: $\lambda = \frac{1.226}{\sqrt{54}} = \frac{1.226}{7.35} \approx 0.167$ nm ✓

Common Mistake

Students sometimes confuse this experiment with G.P. Thomson’s experiment (electron diffraction through thin gold foil). Both confirmed wave nature of electrons — Davisson-Germer used reflection from a nickel crystal surface; G.P. Thomson used transmission through a thin metal film. Both arrived at the same conclusion (same Nobel Prize year, 1937).

Also, do not say “the experiment showed electrons are waves” — more precisely, it showed electrons exhibit wave-like behaviour (diffraction). The complete picture is wave-particle duality: electrons behave as particles in some experiments (photoelectric-type experiments, CRT screens) and as waves in others (diffraction).

JEE and NEET ask: (1) who proposed matter waves — de Broglie; (2) formula for de Broglie wavelength — $\lambda = h/mv = h/p$ ; (3) what did Davisson-Germer experiment demonstrate — wave nature/wave-particle duality of electrons; (4) calculate de Broglie wavelength for electrons accelerated through voltage $V$ — $\lambda = 1.226/\sqrt{V}$ nm. These four points cover all standard exam questions on this topic.

Question

Solution — Step by Step

Why This Works

Alternative Method — Calculating de Broglie Wavelength

Common Mistake

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