Davisson–Germer Experiment — Proof of Matter Waves | Engineering Physics Notes

Davisson & Germer Experiment — Direct Proof of Matter Waves

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Contents 1. Introduction & historical context 2. Experimental setup (diagram + components) 3. Method — what they measured 4. Observations & data 5. Calculations: de-Broglie vs Bragg 6. Why it mattered (significance) 7. FAQ & common confusions

1. Introduction & historical context

In 1924 Louis de Broglie proposed that every particle has an associated wavelength λ = h/p, where h is Planck's constant and p the particle momentum. That bold idea — that matter can behave like waves — needed experimental confirmation. In 1927 C. J. Davisson and L. H. Germer observed electron diffraction from a nickel crystal and measured a wavelength that matched de Broglie's prediction. Their experiment provided direct evidence of the wave nature of particles.

2. Experimental setup (diagram + components)

The experiment was performed inside a vacuum chamber. The main parts were:

• Electron gun: a heated filament produces electrons (thermionic emission) which are accelerated through a potential difference V.
• Collimator: a perforated cylinder that creates a narrow, well-defined beam.
• Nickel single crystal: acts as a diffraction grating (atomic planes).
• Detector (Faraday cylinder) + galvanometer: measures the tiny electron current as a function of angle.

Figure: simplified schematic of the Davisson–Germer apparatus (inline SVG).

3. Method — what they measured

Davisson and Germer produced a fine electron beam and made it strike the nickel single crystal. By rotating the detector around the target and recording the current for different angles (and for different accelerating voltages V), they produced intensity vs. angle curves. A sharp peak in intensity at a particular angle indicates constructive interference — a diffraction maximum — analogous to X-ray diffraction peaks from crystal planes.

Important: The detector measures electrons as a small current. Peaks in that current versus angle are interpreted as diffraction maxima (constructive interference) from atomic planes in the crystal.

4. Observations & data

The key observation was a strong intensity peak for electrons accelerated through V = 54 V at a detector angle φ = 50° (where φ is the angle between the incident beam direction and the direction to the detector). Geometry of the apparatus gives the angle between the lattice planes and the beam used in Bragg's law (we'll call that angle θ below) as 65° for this measurement.

Parameter	Value (as used)
Accelerating potential V	54 V
Detector peak angle φ	50°
Corresponding Bragg angle θ	65°
Interplanar spacing d (from X‑ray data)	0.91 Å

5. Calculations: de‑Broglie prediction vs Bragg (experiment)

a) de‑Broglie (theory)

The de‑Broglie wavelength of an electron accelerated through potential V (non-relativistic approximation) is often written as:

λ = 12.28 /  √V  Å (where V is in volts)

For V = 54 V:

√54 ≈ 7.348469
λ = 12.28 / 7.348469 ≈ 1.67 Å

b) Bragg's law (experiment)

Bragg's law for constructive interference from planes separated by distance d is:

nλ = 2 d sin θ

Using d = 0.91 Å (known independently from X‑ray studies), θ = 65° and n = 1 (first order):

λ = 2 × 0.91 Å × sin(65°) ≈ 1.65 Å

Comparison: λ_deBroglie ≈ 1.67 Å vs λ_{Bragg (measured)} ≈ 1.65 Å — excellent agreement within experimental uncertainty. This match gave direct evidence that electrons display wave-like diffraction with the de‑Broglie wavelength.

Note on approximations: The 12.28/√V form assumes non-relativistic electrons (valid for small V like 54 V). If V grows into the 10⁵ V range, relativistic corrections to momentum should be included.

6. Why this mattered (significance)

• First direct confirmation that matter (electrons) can show diffraction, validating de Broglie's wave hypothesis.
• Bridged concepts between wave optics (Bragg diffraction) and particle physics (electron beams).
• Laid foundations for electron microscopy and many quantum mechanics experiments where wave properties of particles are used.

7. FAQ & common confusions

Q: Were the electrons acting like waves or particles?

A: Both. Detection always registers discrete electrons (particle detection). The diffraction pattern — distribution of many detected electrons over angles — matches interference of waves. Quantum mechanics reconciles this as wavefunctions predicting probability distributions for particle detections.

Q: Why use a crystal instead of a slit?

A: The spacing between atomic planes in crystals (~1 Å) matches the de‑Broglie wavelengths for electrons at modest accelerating voltages. Constructing mechanical slits at that scale was not possible; crystals provide the required periodic structure naturally.

Q: What about relativistic effects?

A: At low voltages (tens to hundreds of volts) electrons are non‑relativistic and the simple formula is fine. For high-energy electrons, use relativistic relations to compute momentum p from kinetic energy.