PARTICLE-LIKE PROPERTIES OF LIGHT (or, of electromagnetic radiation, in general) – continued

1. PARTICLE-LIKE PROPERTIES OF LIGHT (or, of electromagnetic radiation, in general) – continued Let’s summarize what we have said so far: I.Arguments supporting the wave-like nature of light: ●Young’s double-slit experiment; ●Diffraction phenomena (Newton tried to explain diffraction effects using his theory, but his explanations worked only for very simple situations, e.g., “pinhole diffraction”, but not for pronounced effects, such as those seen in experiments with diffraction gratings). ● Maxwell Equations and the results of many experiments that confirm their validity. II. Arguments supporting the particle-like nature of light: ● Photoelectric effect. So far, in this list there is only a single argument in favor of particle-like nature. But the list is not finished yet! More arguments can be added to Part I, as well as to Part II of the above list.

2. Let’s continue the story… Pronounced wave-like properties (interference, diffraction) can be Observed for “soft forms” of electromagnetic radiation (such as “radiofrequency radiation” used in wireless communication, or the waves used in radars – they are called “microwaves” and they are also used in microwave ovens). On the other hand, “soft” electromagnetic radiation does not cause any photoelectric effect – it occurs only for “harder” radiation, i.e., visible light, or even harder than visible light, such as ultraviolet radiation. So, perhaps “softer” EM radiation has a wave-like nature, and with “hardening” it changes to a particle-like nature? This is only partially true: indeed, when the frequency increases (i.e., the wavelength becomes shorter), the particle-like properties are More strongly manifested – but the wave-like properties DON’T GO AWAY, OH, NO! Example: scattering of X-rays by crystals. It is evidently diffraction!

3. About X-rays In 1895, Wilhelm Konrad Röntgen, a German physicist, discovered an entirely new form of radiation. He found that this radiation had many amazing properties. But because its nature was a total mystery for him, he called it “X-rays”. For more than 10 years the “mystery”of X-rays remained unsolved – nonetheless, Röntgen was awarded the first-ever Nobel Prize (1901), and people started using the new “see-throught” radiationinmedical diagnostics and formany other practical purposes. That X-rays offer fantastic new opportunities beacame Clear just weeks after the moment of Discovery: here are examples of early X-rays made in Röntgen’s lab. In one of them you can see the image of bones in the palm of Mrs. Röntgen’s hand. Quick quiz: can you tell, was she an American, or rather you would say she was from Europe?

4. The nature of X-rays remained a “mystery” until… ...another German scientist, Max von Laue, and two British scientists, Bragg father and Bragg son, started shining X-rays on crystals. It turned out that crystals act as 3-dimensional diffraction gratings for X-rays! JAVA Laue : using this link, you can simulate X-ray diffraction images. Examples of X-ray diffraction images (so-called “Lauegrams”): Spahalerite (a mineral) From a “quasicrystal” – do you see that something is unusual?

5. After von Laue’s and Braggs’ experiments, it became clear that X-rays simply belong to the family of electromagnetic waves. The diffraction effects are strongly manifested in crystals, because the typical wavelengths of X-rays (0.1-10 nm) are comparable to the interatomic spacing of crystals. QUESTION: Why we don’t observe diffraction of visible light in crystals? How does diffraction work in crystals? We will try to explain that using math and some helpful pieces of graphic. X-ray scattering by a single atom: Scattered spherical wave Impinging plane wave

6. von Laue’s approach to X-ray diffraction by crystals: Let’s begin with the smallest possible “crystal” one can conceive: namely, one consisting of just two atoms: Important question: what is the phase shift when a wave is reflected from a hard object? (shift between the incident and the reflected or scattered wave)?

7. The Braggs used a different approach: They considered reflection from the planes of atoms in a crystal. Braggs’ approach and results are now widely used, because their Way of handling the problem leads To a particularly simple equation Expressing the conditions at which A reflection may occur: it’s called “the Bragg Law”, “the Bragg cond- tion”, or simply “the Bragg equation”. The Bragg Equation: Here it is shown how the Bragg Eq. is derived: the difference in the “optical paths” of the waves reflected from two adjacent atomic planes must be a whole number of λ-s in order to result in constructive interference. The rest is just high- school trigonometry….

8. Practical example: NaCl crystal (table salt): d = 5.65 nm X-rays:  = 0.154 nm (commonly used wavelength from a “copper” tube. Task: find the diffraction angle of the first reflection, if you rotate the Crystal, starting from θ = 0.