Quantum Physics

Summary 931(a)Figure 28.32 (a) Jack Kilby’s first integrated circuit was tested on September 12, 1958.(b) Integrated circuits continue to shrink in size and price while simultaneously growing incapability.Courtesy of Texas Instruments, Inc(b)Courtesy of Intel Corporationa 1-cm 2 area, with the number of components per square inch having doubledevery year since the integrated circuit was invented.Integrated circuits were invented partly to solve the interconnection problemspawned by the transistor. In the era of vacuum tubes, power and size considerationsof individual components set significant limits on the number of componentsthat could be interconnected in a given circuit. With the advent of the tiny,low-power, highly reliable transistor, design limits on the number of componentsdisappeared and were replaced by the problem of wiring together hundreds ofthousands of components. The magnitude of this problem can be appreciatedwhen we consider that second-generation computers (consisting of discrete transistorsrather than integrated circuits) contained several hundred thousand componentsrequiring more than a million hand-soldered joints to be made andtested.In addition to solving the interconnection problem, integrated circuits possessthe advantages of miniaturization and fast response, two attributes critical forhigh-speed computers. The fast response results from the miniaturization andclose packing of components, because the response time of a circuit depends onthe time it takes for electrical signals traveling at about the speed of light to passfrom one component to another. This time is clearly reduced by packing componentsclosely.SUMMARYTake a practice test by logging intoPhysicsNow at www.cp7e.com and clicking on the Pre-Testlink for this chapter.28.3 The Bohr Theory of Hydrogen &28.4 Modification of the Bohr TheoryThe Bohr model of the atom is successful in describingthe spectra of atomic hydrogen and hydrogenlike ions.One of the basic assumptions of the model is that theelectron can exist only in certain orbits such that its angularmomentum mvr is an integral multiple of , where is Planck’s constant divided by 2. Assuming circularorbits and a Coulomb force of attraction between electronand proton, the energies of the quantum states forhydrogen areE n m ek e 2 e 42 2 1 n 2n 1, 2, 3, . . . [28.12]where k e is the Coulomb constant, e is the charge onthe electron, and n is an integer called a quantumnumber.