This chapter of the video:
• shows how light, which had previously been modelled as a wave, also demonstrates wave–particle duality.
• introduces the formula for the energy of a photon.
• illustrates how this strange behaviour is also seen in protons, neutrons, atoms, and even very large molecules (buckyballs).
• presents the differing opinions of researchers on how big a quantum object can be.

EVIDENCE FOR PHOTONS
The nineteenth century opened with the publication of Young’s double-slit experiment, which firmly established the wave nature of light. As the century drew to a close there were several experiments that pointed to the need for a different model. By 1905, Einstein was using a particle model for light in his explanation of the photoelectric effect. The double-slit experiment showed that light came in packets whose energy could be calculated by the equation

Note how the variables in this equation illustrate the wave–particle duality of light. A photon, which is detected as a localized object like a particle, has an energy that is proportional to its frequency, which is a wave-like property. The two aspects are connected by Planck’s constant, the same constant that is in the de Broglie wavelength equation, . The de Broglie equation holds for all quantum objects, including photons, and therefore a photon has momentum even though it has no mass.

A demonstration of Young’s double-slit experiment with individual photons was done by Geoffrey Ingram Taylor in 1909. He used extremely faint light, so that there was only one photon in the apparatus at a time. The light was so faint that it required a three-month exposure time before the many individual photons were able to form an interference pattern.

WAVE-PARTICLE DUALITY AND LIGHT
All of the wave-like properties of light can be demonstrated using individual photons. This means that all of the demonstrations and experiments that we do with light have quantum physics at their core. For example, thin-film interference seems quite reasonable as a wave phenomenon; part of the wave reflects from the top surface of the thin film and part reflects from the bottom. These two parts interfere with each other to produce maxima and minima that vary with the thickness of the film. But this interference pattern forms even for only one photon at a time. How can a single photon do this? It is the same counter intuitive result that is found in the double-slit experiment.

The model for light scientists use often depends on the energy of the radiation with which they are working. Individual photons are easiest to detect if they are high energy, and so physicists who work with low-energy radio waves rarely consider light’s particle-like behaviour, and physicists who deal with high-energy gamma radiation rarely see the wave-like behaviour.

THE QUANTUM NATURE OF LARGE OBJECTS
Larger objects should also have de Broglie wavelengths, but these are much harder to demonstrate. Their wavelengths are smaller because their mass is greater. Recall the de Broglie equation:



For example, buckminsterfullerene, or buckyballs, are made of 60 carbon atoms, so each one is about 600 000 times more massive than an electron. In order to make their wavelengths large enough to be detected, physicists had them travel much more slowly—200 m/s rather than 120 000 000 m/s. Even so, the wavelength of the balls was only 0.0025 nm, which is 400 times smaller than the 1 nm size of the molecule itself!

It gets more difficult to demonstrate interference as the wavelengths get smaller. Separation between the maxima is given by



We can compensate somewhat for the tiny wavelength by using a very small slit separation, d. The slits in the buckyball experiment were 50 nm wide and separated by 100 nm. To make the separation of maxima even clearer, physicists used a diffraction grating with many slits, rather than just two. This does not change the separation between maxima, but it does make the maxima more concentrated and the minima more spread out (see Figure 3.4).

The results of the buckyball experiment are shown in Figure 3.5. The graphs show the results without a diffraction grating (top) and with (bottom). Note that there are only two interference maxima produced beyond the central one and these are really not all that clear. This shows how difficult it is to demonstrate the interference of such a “large” object. The same physicists have also shown interference with a fluorinated buckyball made of 60 carbon atoms plus 70 fluorine atoms, and they are trying for larger molecules. The physicists in the video disagree as to whether there is a theoretical limit or just a practical, technological limit to showing quantum effects with large objects. The answer is not known.