Quantum Physics

882 Chapter 27 Quantum Physics–IncomingelectronNucleus oftarget atom+EmittedphotonDeflectedlower energyelectronFigure 27.10 An electron passingnear a charged target atom experiencesan acceleration, and a photonis emitted in the process.–hfAPPLICATIONUsing X-Rays to Study theWork of Master Painterscharged nucleus contained in the target material, it is deflected from its path becauseof its electrical attraction to the nucleus; hence, it undergoes an acceleration.An analysis from classical physics shows that any charged particle will emit electromagneticradiation when it is accelerated. (An example of this phenomenon is theproduction of electromagnetic waves by accelerated charges in a radio antenna, asdescribed in Chapter 21.) According to quantum theory, this radiation must appearin the form of photons. Because the radiated photon shown in Figure 27.10 carriesenergy, the electron must lose kinetic energy because of its encounter with thetarget nucleus. An extreme example would consist of the electron losing allof its energy in a single collision. In this case, the initial energy of the electron(eV ) is transformed completely into the energy of the photon (hf max ). Inequation form,eV hf max [27.8]where eV is the energy of the electron after it has been accelerated through apotential difference of V volts and e is the charge on the electron. This says thatthe shortest wavelength radiation that can be produced is min hc[27.9]eVThe reason that not all the radiation produced has this particular wavelength isbecause many of the electrons aren’t stopped in a single collision. This results inthe production of the continuous spectrum of wavelengths.Interesting insights into the process of painting and revising a masterpiece arebeing revealed by x-rays. Long wavelength x-rays are absorbed in varying degreesby some paints, such as those having lead, cadmium, chromium, or cobalt as abase. The x-ray interactions with the paints give contrast, because the differentelements in the paints have different electron densities. Also, thicker layers willabsorb more than thin layers. To examine a painting by an old master, a film isplaced behind it while it is x-rayed from the front. Ghost outlines of earlier paintingsand earlier forms of the final masterpiece are sometimes revealed when thefilm is developed.hc minEXAMPLE 27.4 An X-Ray TubeGoal Calculate the minimum x-ray wavelength due to accelerated electrons.Problem Medical x-ray machines typically operate at a potential difference of 1.00 10 5 V. Calculate the minimumwavelength their x-ray tubes produce when electrons are accelerated through this potential difference.Strategy The minimum wavelength corresponds to the most energetic photons. Substitute the given potential differenceinto Equation 27.9.SolutionSubstitute into Equation 27.9: min hceV (6.63 1034 Js)(3.00 10 8 m/s)(1.60 10 19 C)(1.00 10 5 V) 1.24 10 11 mRemarks X-ray tubes generally operate with half the voltage with respect to Earth, 50 000 V, applied to theanode, and the other half, 50 000 V, applied to the cathode. This lengthens tube lifetime by reducing the probabilityof voltage breakthroughs.