Page 493 - Physics Coursebook 2015 (A level)

Chapter 30: Quantum physics
BOX 30.3: Investigating electron diffraction
If you have access to an electron diffraction tube (Figure 30.25), you can see for yourself how a beam of electrons is diffracted. The electron gun at one end of the tube produces a beam of electrons.
By changing the voltage between the anode and
the cathode, you can change the energy of the electrons, and hence their speed. The beam strikes a graphite target, and a diffraction pattern appears on the screen at the other end of the tube.
+6 V
0V
cathode
+ 5 kV
Figure 30.23 When a beam of electrons passes through a graphite film, as in this vacuum tube, a diffraction pattern is produced on the phosphor screen.
particles. Diffraction is a property of waves. Hence the rings can only be explained if the electrons pass through the graphite film as a wave. The electrons are diffracted by the carbon atoms and the spacing between the layers of carbon atoms. The atomic layers of carbon behave like a diffraction grating with many slits. The electrons show diffraction effects because their de Broglie wavelength λ is similar to the spacing between the atomic layers.
This experiment shows that electrons appear to travel as waves. If we look a little more closely at the results of the experiment, we find something else even more surprising. The phosphor screen gives a flash of light for each electron that hits it. These flashes build up to give the diffraction pattern (Figure 30.24). But if we see flashes at particular points on the screen, are we not seeing individual electrons – in other words, are we not observing particles?
pattern builds up as experiment proceeds
Figure 30.24 The speckled diffraction pattern shows that it arises from many individual electrons striking the screen.
θ
phosphor screen
Figure 30.25 Electrons are accelerated from the cathode to the anode; they form a beam which is diffracted as it passes through the graphite film.
You can use an electron diffraction tube to investigate how the wavelength of the electrons depends on their speed. Qualitatively, you should find that increasing the anode–cathode voltage makes the pattern of diffraction rings shrink. The electrons have more kinetic energy (they are faster); the shrinking pattern shows that their wavelength has decreased. You can find the wavelength λ of the electrons by measuring the angle θ at which they are diffracted:
λ = 2d sin θ
where d is the spacing of the atomic layers of graphite.
You can find the speed of the electrons from the anode–cathode voltage V:
12 mv2 = eV
anode graphite
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