Davisson-Germer experiment: proof of matter waves
Electrons of 54 eV scattered by a nickel crystal gave a strong beam at 50°, just as waves of 1.67 Å would. This proved that electrons behave as waves.
The apparatus and method
- 1A heated filament F gives out electrons. An accelerating voltage gives them a chosen energy.
- 2The electrons pass through narrow slits in metal diaphragms, which make a fine, parallel beam. Together these form an electron gun.
- 3The beam falls at right angles on a single crystal of nickel.
- 4A movable detector (collector), joined to a galvanometer, measures how many electrons are scattered at each angle θ.
- 5The whole apparatus is kept in an evacuated chamber.
- 6★The voltage is changed in steps, and for each energy the scattered intensity is measured at many angles.
★ key step
What they found
The scattered electrons did not spread out evenly. With an accelerating voltage of 54 V, a strong peak appeared at a scattering angle of 50°. Particles simply bouncing off atoms could not give such a sharp peak. Waves diffracted by the rows of atoms could. The wavelength found from the crystal spacing agreed closely with de Broglie's λ = h/p. So electrons really behave as waves.
Worked example: wavelength of 54 eV electrons
In the Davisson-Germer experiment, the peak appeared for electrons of energy 54 eV. Find their de Broglie wavelength. (h = 6.63 × 10⁻³⁴ J s, m = 9.1 × 10⁻³¹ kg, 1 eV = 1.6 × 10⁻¹⁹ J)
- Formula: λ = h/√(2mE), where E is the kinetic energy.
- E = 54 × 1.6 × 10⁻¹⁹ J = 8.64 × 10⁻¹⁸ J.
- 2mE = 2 × 9.1 × 10⁻³¹ × 8.64 × 10⁻¹⁸ = 1.57 × 10⁻⁴⁷.
- √(2mE) = 3.96 × 10⁻²⁴ kg m/s.
- λ = 6.63 × 10⁻³⁴ ÷ 3.96 × 10⁻²⁴ = 1.67 × 10⁻¹⁰ m = 1.67 Å.
- Check with the shortcut: 12.3/√54 = 12.3/7.35 ≈ 1.67 Å.
λ ≈ 1.67 Å, about the spacing between rows of atoms in the nickel crystal
How to draw the Davisson-Germer apparatus
- On the left, draw a small coil labelled filament F, joined to a low-tension (L.T.) battery.
- In front of it, draw a few plates with slits labelled diaphragms; bracket them as electron gun, joined to a high-tension (H.T.) battery.
- Draw an arrow for the electron beam falling on a block labelled nickel crystal (target).
- Draw a second arrow leaving the crystal at angle θ to the incoming beam, ending at a box labelled movable detector, joined to a galvanometer.
- Draw a dashed line round everything labelled evacuated chamber.
- Beside it, sketch detector current against electron energy with a sharp peak at 54 eV (θ = 50°).
For reading only: the electron microscope (not set in the exam)
Fast electrons have wavelengths far shorter than light. A microscope shows finer detail when the wavelength is shorter. So an electron microscope, which focuses an electron beam with magnetic lenses, shows far finer detail than a light microscope. A light microscope reaches about 1000 times magnification. An electron microscope can show viruses and the tiny parts inside a cell.
Electron microscopes in Indian research laboratories and hospitals use the wave nature of electrons. They show viruses, bacteria and the fine structure of new materials, far beyond what a light microscope can see.
3 marks: “Describe the Davisson-Germer experiment. What did it prove?” An electron gun (filament, accelerating voltage, slits) sends a fine beam onto a nickel crystal in vacuum; a movable detector measures scattering at each angle. At 54 V a sharp peak appeared at 50°, as for waves of 1.67 Å diffracted by the crystal. It proved the wave nature of electrons (de Broglie waves).
2 marks: “Why did Davisson and Germer fire electrons at a nickel crystal, and what idea is the experiment based on?” Aim: to verify that electrons behave as waves (de Broglie's hypothesis). Principle: electron waves are diffracted by the regular arrangement of atoms in a crystal.
1 marks: “Which crystal was used as the target in the Davisson-Germer experiment?” A single crystal of nickel.
54, 50, 1.67: 54 eV electrons, a peak at 50°, a wavelength of 1.67 Å.