QUANTUM MECHANICS (see Chapter 14) As with nuclear physics (fission and fusion) you've asked very few questions regarding this area. In the broadest sense, quantum mechanics attempts to describe physical behaviour on a very small scale (atomic or subatomic). So, you wouldn't need quantum mechanics to describe the motion of a falling rock, but you can use it to explain how “current” (i.e. moving electrons) can be created within a “semiconductor” (a material which doesn't normally carry current, but can do so under certain conditions). Of course, everything could be studied on an atomic or subatomic scale (even if it doesn't have to be), which means that quantum mechanics is an underlying aspect of everything! Quantum physics can be theoretically complex (and can require very advanced mathematical techniques), so we won't get into too much depth here. There are some very simple underlying ideas which can easily be presented, however. The Dual Wave/Particle Nature of Light You have recently heard about the often nasty historical debate (led by Huygen and Newton and their followers) on whether light is an electromagnetic wave or a particle (photon). Long after this issue appeared to have been settled in favour of the wave side, it turns out that light actually has a “dual nature”. That is, light exhibits characteristics of both waves and particles! Describing the emission of light by an excited atom, in which an electron first jumps to a higher energy level and then jumps back down with the ejection of a photon (a light “particle”) is obviously a quantum mechanical explanation. It turns out that the energy E (in Joules) associated with a particular photon is given by the equation E = hf, where h = 6.63 10-34 J-s is Planck's constant and f is the “wave frequency” associated with the photon. (This frequency may correspond not only to visible light, but also to any other electromagnetic wave such as ultraviolet, infrared, microwaves, etc.) Example Suppose a particular lightbulb produces 10 watts (10 Joules/s) of red light with wavelength 663 nm. Each photon has energy 6.63 10 34 3.00 10 8 19 E hf 3 . 00 10 J. 663 10 9 hc So, to produce 10 J each second would require the emission of 10 3.33 1019 photons. 19 3.00 10 (Note that each photon releases a tiny “pulse” of light, but with so many emissions each second, the resulting light would appear “continuous”.) The Photoelectric Effect In the above example, matter (consisting of large numbers of atoms) gives off light as a result of absorbing energy. It turns out that matter can also emit charged particles (electrons) by absorbing energy. This important phenomenon is called the photoelectric effect. Specifically, if you shine light of certain frequencies on metals, they will emit electrons. (The mechanism here is essentially that absorbed energy, in the form of photons, can cause electrons previously held in the crystal lattice of the metal to escape the metal altogether). The photoelectric effect is the principle underlying the use of photovoltaic cells, i.e. “solar cells”, which absorb sunlight or other visible light and, through the release of electrons, produce electric current which can be used to operate switches, processors, motors, etc. Note that the rate at which electrons are emitted has much more to do with the frequency of the incident light than its intensity. Light whose frequency is less than the required minimum will produce no emissions whatsoever, regardless of its brightness, whereas even very weak light of sufficiently high frequency will produce some ejected electrons. Matter Waves The discovery that light (initially shown to be a wave) can be considered a particle soon led to the parallel discovery that matter (i.e. particles) can also exhibit wave behaviour. In other words, not only can waves act like particles, but particles can act like waves! The wavelike behaviour of matter is referred to as matter waves, and is governed by the simple equation h h p mv . This equation can be applied to macroscopic (large scale) objects, though it is only meaningful for subatomic particles. Example For a 66.3 kg person walking at 1 m/s, the corresponding matter wave would have a wavelength of h 6.63 1034 1035 m. mv 66.31 Example On the other hand, for a electron travelling at a (typical) speed of 107 m/s, h 6.63 1034 11 10 7 . 3 10 10 m. mv 9.111031 107 This is about the diameter of an atom. Basically, these two examples suggest that the wavelength of a matter wave can be thought of as the “region of influence” of the matter itself. The region of influence associated with a large-scale object is too small to make any difference (i.e. to be detected or measured) while the region of influence associated with an electron is (not surprisingly) comparable to the size of an atom, whose structure and behaviour is largely determined by the presence of electrons! The Uncertainty Principle One of the most interesting ideas of quantum mechanics is the uncertainty principle, first proposed by Heisenberg. Essentially, this says that (at least for very small scale objects) we can never know both a particle's location and its momentum precisely. Rather, the more precisely you know one, the less precisely you can know the other. Mathematically, the uncertainty principle is expressed as px h . This says that a reduction in the uncertainty in a body's speed (i.e. uncertainty in its momentum) will be accompanied by increased uncertainty in its location. This isn't really a significant problem for large-scale (macroscopic) bodies undergoing “everyday” motions, since Planck's constant is so small that both momentum and location can have very small uncertainties (and thus both be known quite accurately). Imagine trying to simultaneously determine the location and momentum of a very tiny moving particle, however. To detect the particle's position, a photon or electron must be sent to it, bounce off it, and return to your measuring instrument. Since the target is small, the momentum of the photon or electron which interacts with it will actually change the target particle's motion thereafter, slightly. Furthermore, because it takes a finite (but small) amount of time for the photon or electron to return to the measuring instrument, it will no longer be at that location by the time the measurement is complete. That is, the very act of observing the particle changed its momentum, and its actual location has also changed by the time the measured location is recorded. Applications of Quantum Mechanics The applications of quantum theory in society today are literally too many to list. The photoelectric effect is responsible not only for the technology of photovoltaic cells, but also for the physics behind transistors and other semiconductors found in virtually all of today's electronic devices. Matter wave theory is used in imaging devices like electron microscopes, which use “electron waves” rather than light waves. The integrated circuits and microprocessor chips found in today's computers and many other electronic instruments can combine the equivalent of millions and even billions of individual transistors within a very small space. Without this ability to miniaturize electronic circuitry, technologies like cell phones, MP3 players, communication satellites and the space shuttle would all have been impossible.