| Light as Particles.
The Photoelectric Effect: An Analogy.
In an earlier section, I spent considerable time persuading you that
Oddly, I need now to persuade you that light can be said to behave in corpuscular fashion - that is, like a little packet of energy, which you can visualise as a small 'bullet,' the technical word for which is a photon. The really good evidence for this comes from something called the photoelectric effect. (Einstein won the Nobel Prize for explaining this effect.)
In class, I explained the photoelectric effect via the following analogy.
First, visualize piling up bricks in some regularly ordered fashion to build a wall, but don't use any mortar, so that the bricks are independent.
Now imagine flinging a ping-pong ball at high speed -- say, 90 miles an hour -- against this wall. The ping-pong ball would surely not have enough energy to dislodge a brick. (Indeed, the ball itself would suffer serious damage, but that is not the point of the analogy.)
If you threw a somewhat heavier ball, like a tennis ball, at the wall at that same high speed, it probably would still not dislodge a brick.
Many major league pitchers can throw a baseball at ninety miles an hour, and I expect, without having tried the experiment, that one of them could cause a brick to come loose and be pushed out of the back of the wall.
Now imagine something considerably more massive: a ball of the very densest steel fired towards the wall at the same high speed. Not only would it pop a brick loose, but it would probably cause any brick it hit to fly back out of the wall with some vigour.
How do these situations differ? The answer is that the different balls, having different masses, have different amounts of energy, even though they are all travelling at the same speed (90 miles per hour, in this discussion). The kinetic energy (the energy of motion) of any object is given by the simple relationship:
Kinetic energy = 1/2 x (the mass of the object) x (the square of its speed) so more massive objects have more energy if the speeds are the same. A truck running into a highway guardrail at 100 km/h will do more damage than a much lighter motorcycle travelling at the same speed, and the crumpling of the metal is a result of the dissipation of all that energy of motion.
The Photoelectric Effect: The Reality .Now think about a comparable (and very famous) physics experiment, one in which we shine light of various colours onto materials of various kinds. We observe that under certain circumstances -- the right materials, the right colour of light -- electrons are dislodged and fly off with some speed. Moreover, the speed with which the electrons fly off depends very strongly on the colour of the light which is used. This phenomenon obviously requires energy to knock the electrons free of their atoms and to set them in motion. Where does this energy come from? And how can we understand the speeds which are imparted to the released electrons? You could be excused for thinking that the total energy of the source of light must be the determining factor. Remarkably, that turns out not to be the case! The total amount of energy landing on the sheet of material is indeed determined by the brightness of the light, but the experiment reveals that no electrons whatsoever are liberated when you shine red light on the material, regardless of its brightness. (Indeed, you could go to the expense of building the brightest red light the world has ever seen and still fail to liberate those stubborn electrons.) Amazingly, though, the instant you shine blue light on the surface, even just as a faint glimmer, electrons are dislodged. Furthermore, ultraviolet light (which is of still shorter wavelength than the blue light) dislodges electrons which are found to be moving considerably faster than those which are dislodged by blue light. What can all this mean? Well, the experiment tells us that it is not sufficient merely to visualise light as a wave, or bunch of waves, with a total amount of energy spread all over the place like water waves lapping up on shore. Inevitably, it seems that light is particle-like as well, with the red photons being analogous to our ping-pong balls, and the blue and ultraviolet light corresponding to the more energetic balls, the baseball and dense steel ball. No matter how many ping-pong balls you fling at the wall, or how much red light you shine on the material, no bricks or electrons get knocked out. But a single baseball, or a single blue photon, can dislodge a brick or electron. A single steel ball, or a single ultraviolet photon, will liberate a brick or electron which is itself moving with considerable speed. This homespun analogy is too simple in some respects, but the conclusion is correct. Light of a certain wavelength (or colour) can be visualized as a little packet of energy, with the energy depending on the colour of the light. In fact, there is a simple formula describing this (see page 157 of the text): (energy in a photon) = (Planck's constant) x (frequency of the light) = h f where ``Planck's constant,'' symbolised by a lower-case h, is a physical constant -- one of quite small size, in fact, since a single photon contains very little energy by human standards. Indeed, a simple calculation reveals that a single 100-Watt light bulb emits more than a billion billion photons of visible light per second, flying off in all directions! Since gamma rays are the highest-frequency forms of electromagnetic radiation, this formula implies that they are far more energetic than other forms of light. And this is true. Gamma rays can be so energetic that, if they are absorbed by human cells, they can disrupt the integrity of DNA molecules and lead to mutations, cancers, birth defects, and the like. (This is the principal danger of radioactive contamination, as with the Chernobyl catastrophe, during which a lot of nuclear waste products escaped confinement.) Meanwhile, however, the room we are in is constantly flooded with uncountable numbers of low-energy radio-wavelength photons which do us no harm whatsoever. Since blue light is of higher frequency than red light, blue photons carry more energy. Thus, if a blue photon enters your eye it has enough energy to cause certain chemical changes in various pigments in your retina. The changes create electrical signals which are transmitted to the brain: you experience the sensation of seeing the colour blue. A red photon is not energetic enough to make those particular changes, but some other chemistry happens, and you see red. An important reminder: When you reconsider the various balls in the analogy above, you will realise that they differ from one another in mass, but could also have been moving at different speeds, which would also affect their total energy. For instance, a bullet flying towards you at extremely high speed will cause far greater damage to your person than a considerably heavier baseball thrown at much lower speed since the bullet carries more energy by far. All photons of light, however, travel at the same speed in the vacuum of space, so the differences in their energies have nothing to do with their speeds. For light, it is the frequency (or equivalently the colour) that matters.
The Wave-Particle Duality.Note that the equation presented in the previous section has a deep philosophical ambiguity in it. We talk about the energy in the photon as though it were a small discrete lump, but we also refer to the frequency of the light, which reaffirms our interpretation of light as having an associated frequency and wavelength, like any wave phenomenon. The tension between these points of view is a hard one to resolve. It is difficult to imagine something which has both wave-like and particle-like properties! Yet in modern physics that is effectively just what one must do. In some contexts, like the way light diffracts when it passes through a small hole, the 'waviness' of the light is what matters. In other contexts, like the photoelectric effect, it is its 'lumpiness' that is important. Just as remarkably, this duality extends to ordinary matter as well! There are contexts in which particles of matter -- electrons, for instance -- behave as though they are wavelike rather than like little billiard balls, as one usually visualizes them. By the way, here is a helpful way of remembering that blue photons, of higher frequency than red, carry extra energy. Imagine two people walking down the road at the same speed, side by side. Suppose that one of them is very passive, walking along in quiet fashion, while the other is gesticulating wildly, waving his or her arms up and down rapidly (that is, `at high frequency'). I think that you would agree that the second person seems more animated and energetic, in some metaphorical sense of the word, than the first. Think of the photons in this way, and you will keep the dependence of energy, frequency and wavelength correct in your mind. Higher frequencies and shorter wavelengths correspond to greater energies! Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Sunday, 24 January, 2021.)