The Davisson–Germer experiment
Firing electrons at a crystal
This experiment is no longer in the current NCERT syllabus, but it is a classic, and it is useful for competitive exams. It is the experiment that showed de Broglie was right: electrons really do behave as waves.
In 1927, C. J. Davisson and L. H. Germer in the United States fired a beam of electrons at a nickel crystal. At about the same time, G. P. Thomson in Scotland passed electrons through thin metal films. Both saw electrons being diffracted.
Here is the Davisson–Germer apparatus. The electron gun has a tungsten filament, coated with barium oxide and heated by a low-voltage supply. Electrons boil off it by thermionic emission.
A high-voltage supply accelerates the electrons through a chosen potential difference V. They then pass through a cylinder with fine holes along its axis, which makes a fine, parallel beam.
The beam falls straight onto the surface of a nickel crystal. The atoms of the crystal scatter the electrons in all directions.
A detector, or collector, picks up the electrons scattered in one direction. It is joined to a sensitive galvanometer, whose deflection tells us the intensity of the scattered beam.
The detector can be moved around a circular scale, so we can measure the intensity at different scattering angles θ, the angle between the incident beam and the scattered beam. The whole apparatus is inside an evacuated chamber.
For each accelerating voltage, the intensity is measured at many angles and drawn as a polar graph around the crystal: the farther the curve from the crystal, the stronger the scattering in that direction.
The peak at 54 volts
Watch the polar graphs as the voltage goes up: 44 volts, 48 volts, 54 volts, 64 volts, 68 volts. At 44 volts there is a small bump. It grows, and at 54 volts it becomes a sharp peak, at a scattering angle of 50°. Then it fades again.
A peak in one particular direction is what waves do when they are diffracted. It comes from constructive interference of the electron waves scattered by the regularly spaced layers of atoms in the crystal.
From the diffraction measurements, the wavelength of the electron waves came out as 0.165 nanometre.
One way to see where this comes from: the rows of nickel atoms on the surface are d = 0.215 nanometre apart, and they act like a grating. d sin θ equals λ gives 0.215 times sin 50°, which is 0.215 × 0.766, or 0.165 nanometre.
Now de Broglie’s prediction. For an electron accelerated through V volts, λ equals h over p, which is 1.227 over √V nanometres.
With V = 54 volts, √54 is about 7.35, and λ equals 1.227 divided by 7.35: 0.167 nanometre.
Measured, 0.165 nanometre. Predicted, 0.167 nanometre. They agree to about one percent. The electrons were diffracted exactly as waves of wavelength h over p would be.
At a higher voltage, the electrons have more momentum and a shorter wavelength, so the peak moves to a smaller angle. The experiment confirmed the wave nature of electrons, and later, neutrons, atoms and molecules were diffracted too.
Try it: the Davisson–Germer experiment
- Drag the detector around the scale (or use the θ slider) and watch the detector reading change.
- Raise V from 44 V to 68 V. The bump in the polar plot is most pronounced at 54 V. Press “Go to the peak”: it is at about 50°.
- At the peak, compare λ = d sin θ (from the diffraction) with λ = 1.227/√V (de Broglie). They agree to about 1%.
- At higher voltages the peak moves to smaller angles, because the wavelength is shorter.
The predicted wavelength
What is the de Broglie wavelength of electrons accelerated through 54 V?
- 0.167 nm
- 1.67 nm
- 0.023 nm
- 9.02 nm
Answer
A. λ = 1.227/√V nm = 1.227/√54 = 1.227/7.35 = 0.167 nm. Dividing by V instead of √V gives 0.023 nm; multiplying by √V gives 9.02 nm. Davisson and Germer measured 0.165 nm, in close agreement.
A higher voltage
The accelerating voltage is raised from 54 V to 64 V. Where does the diffraction peak move?
- To a smaller scattering angle
- To a larger scattering angle
- It stays at 50°
- It disappears, because the electrons are too fast to diffract
Answer
A. A higher voltage gives more momentum and so a shorter wavelength: λ = 1.227/√64 = 0.153 nm. With d sin θ = λ and d = 0.215 nm, sin θ ≈ 0.153/0.215 ≈ 0.71, so θ ≈ 45°: a smaller angle than 50°.
Summary
- de Broglie wavelength (electron through V):
λ = h/√(2meV) = 1.227/√V nm - At 54 V:
λ = 0.167 nm (predicted), 0.165 nm (measured) - Surface rows as a grating:
d sin θ = λ, d = 0.215 nm
- Extra topic, beyond the current NCERT syllabus. Davisson and Germer (1927) scattered electrons from a nickel crystal and measured the intensity at different angles.
- A sharp peak appeared at 54 V and a scattering angle of 50°, caused by constructive interference of electron waves from the regularly spaced atoms.
- The measured wavelength, 0.165 nm, agrees closely with de Broglie’s h/p = 0.167 nm: electrons behave as waves.
- Higher voltage, shorter λ, peak at a smaller angle.