The Davisson-Germer experiment, carried out by Clinton Davisson and Lester Germer in 1927, was the first direct experimental confirmation of de Broglie's matter-wave hypothesis. Their apparatus heated a filament with a low-tension battery to emit electrons by thermionic emission, accelerated these electrons through a known potential difference using a high-tension battery, collimated them into a narrow beam using two thin aluminium diaphragms, and directed this beam onto a single crystal of nickel. Because a crystal's regularly spaced atomic planes can act as a natural three-dimensional diffraction grating for any wave whose wavelength is comparable to that spacing -- and an electron's de Broglie wavelength, at typical laboratory accelerating voltages, is indeed of that same order (10−10 m) -- any genuine wave character in the electron beam should show up as a diffraction pattern in how the beam scatters off the crystal. …
Step 1. In 1927, Clinton Davisson and Lester Germer fired a beam of electrons, accelerated through a known potential, at a single crystal of nickel.
Step 2. The intensity of the scattered electron beam, measured as a function of scattering angle, showed a sharp peak at a specific angle (50° at 54 V accelerating voltage).
Step 3. Such a sharp intensity peak is the signature of diffraction -- constructive interference of waves scattered from successive atomic layers of the crystal -- a phenomenon that only makes sense if the electron beam has a genuine wave character. …
Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.
CBSE 2020Set ANNUAL5 marks
Q.(a) Describe Davisson-Germer experiment which demonstrated the wave nature of electrons.
OR
(b)
(i) Derive an expression for the orbital energy of an electron in hydrogen atom using Bohr theory.
(ii) An electron in Bohr's hydrogen atom has an energy of −3.4 eV. What is the angular momentum of the electron ?
›Reveal solutionSolution
(a) The Davisson-Germer experiment found a sharp scattered-electron intensity peak matching de Broglie's predicted diffraction wavelength, confirming electron wave nature; (b) Bohr's energy formula gives En=−13.6/n2 eV, and for E=−3.4 eV (n=2), the angular momentum is L=h/π≈2.11×10−34 J s. Both alternatives answered below.
(a) Davisson-Germer experiment
Apparatus. An electron gun (heated filament + accelerating potential V) produces a fine beam of electrons directed at a nickel crystal target. A movable detector, positioned at various scattering angles θ from the incident beam, measures the intensity of electrons scattered by the crystal.
Observation. For ordinary (non-crystalline) scattering, intensity would vary smoothly with angle. Instead, at an accelerating voltage of 54 V, a pronounced, sharp peak in scattered electron intensity was observed at a scattering angle of 50° — behaviour characteristic of diffraction, not simple particle scattering.
Interpretation. The nickel crystal's regularly spaced atomic planes act like a diffraction grating. Using Bragg's law for the observed diffraction peak, the wavelength associated with the 54 V electrons works out to about 1.65 Å.
Comparison with de Broglie's hypothesis. For an electron accelerated through 54 V, the predicted de Broglie wavelength is
λ=2meVh≈1.67A˚
which matches the experimentally observed value (1.65 Å) very closely.
This agreement provided direct, quantitative experimental confirmation that electrons — usually thought of as particles — exhibit wave-like diffraction behaviour, verifying de Broglie's hypothesis.
(b)(i) Orbital energy of the electron in hydrogen atom (Bohr theory)
For an electron of charge −e orbiting a nucleus of charge +e in the nth Bohr orbit of radius rn:
Coulomb attraction provides the centripetal force: