Electron diffraction and the de Broglie wavelength – diffraction tube, double slit, electron microscope
PhysicsQuantum & Nuclear PhysicsAges 17–18
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Sign in to playAn electron diffraction tube with a graphite target: change the accelerating voltage V and watch the rings on the fluorescent screen shrink as V rises, measure the ring diameters with a ring gauge, record a table, plot D against 1/√V and work out the wavelength λ = h/√(2meV) and the spacing d of the atomic planes. Compare with the rings made by X-rays of the same wavelength and bring a magnet near the tube. The Double slit screen sends electrons one at a time and builds up interference fringes; the Microscope screen compares the resolution of a light microscope and a transmission electron microscope.
Lesson: Wave–particle duality: the de Broglie wavelength, electron diffraction, electron interference at a double slit, the electron microscope
What it shows
De Broglie proposed that every particle has a wavelength λ = h/p. Electrons accelerated through a voltage V have momentum p = √(2meV), so λ = h/√(2meV), a few picometres for a few kilovolts. A thin polycrystalline graphite film acts like a diffraction grating: Bragg reflection 2d sinθ = λ at two sets of atomic planes sends electrons into cones that make two rings on the screen. Raising V shortens λ and shrinks the rings. Electrons sent one at a time through a double slit land as particles yet build up wave fringes. Short wavelengths also give electron microscopes their high resolution.
How to use
On the Diffraction tube tab, set Voltage V, drag on the screen or use Ring gauge D to fit the dashed circle over a ring, choose Ring measured and press Record. Repeat at several voltages and read d from the fitted lines. Try Compare with X-rays with Same wavelength, and Bring a magnet near. On the Double slit tab, change Slits, Slit separation d and Emission rate. On the Microscope tab, change the TEM voltage.
Parameters you can change
- Screen Electron diffraction tube, Electrons through a double slit, Electron microscope
- Accelerating voltage V (diffraction tube) 1.5–5 kV
- Show the graphite lattice
- Bring a magnet near the tube
- Compare with X-rays
- X-ray photon energy 20–120 keV
- Accelerating voltage V (double slit) 10–100 kV
- Slit separation d 0.5–4 µm
- Slits Both slits open, One slit closed, Detector shows which slit
- Electron emission rate Slow (one at a time), Medium, Fast
- Show the predicted distribution
- Accelerating voltage of the electron microscope 10–300 kV
- Wavelength of light in the light microscope 400–700 nm
Questions to explore
- Why do the rings get smaller when the accelerating voltage is increased?
- Why does a magnet shift the electron rings but not the X-ray rings?
- Why do the fringes disappear when a detector shows which slit each electron passed through?
