Quantum Physics

Problems 90151.time of 5.00 ms. Find (a) Johnny’s de Broglie wavelengthat this moment, (b) the uncertainty of hiskinetic energy measurement during such a period oftime, and (c) the percent error caused by such anuncertainty.Photons of wavelength 450 nm are incident on ametal. The most energetic electrons ejected from themetal are bent into a circular arc of radius 20.0 cm by amagnetic field with a magnitude of 2.00 10 5 T.What is the work function of the metal?52. A 200-MeV photon is scattered at 40.0° by a free protonthat is initially at rest. Find the energy (in MeV) ofthe scattered photon.53. A light source of wavelength illuminates a metal andejects photoelectrons with a maximum kineticenergy of 1.00 eV. A second light source of wavelength/2 ejects photoelectrons with a maximum kineticenergy of 4.00 eV. What is the work function of themetal?54. Red light of wavelength 670 nm produces photoelectronsfrom a certain photoemissive material. Greenlight of wavelength 520 nm produces photoelectronsfrom the same material with 1.50 times the maximumkinetic energy. What is the material’s workfunction?55.How fast must an electron be moving if all its kineticenergy is lost to a single x-ray photon (a) at the highend of the x-ray electromagnetic spectrum with awavelength of 1.00 10 8 m; (b) at the low end ofthe x-ray electromagnetic spectrum with a wavelengthof 1.00 10 13 m?56. Show that if an electron were confined inside anatomic nucleus of diameter 2.0 10 15 m, it wouldhave to be moving relativistically, while a proton confinedto the same nucleus can be moving at less thanone-tenth the speed of light.57. A photon strikes a metal with a work function andproduces a photoelectron with a de Broglie wavelengthequal to the wavelength of the original photon.(a) Show that the energy of this photon must havebeen given byE (m e c 2 /2)m e c 2 where m e is the mass of the electron. [Hint : Beginwith the conservation of energy, E m e c 2 √(pc)2 (m e c 2)2.] (b) If one of these photons strikesplatinum ( 6.35 eV), determine the resultingmaximum speed of the photoelectron that isemitted.58. In a Compton scattering event, the scattered photonhas an energy of 120.0 keV and the recoilingelectron has a kinetic energy of 40.0 keV. Find(a) the wavelength of the incident photon, (b) theangle at which the photon is scattered, and (c) therecoil angle of the electron. [Hint : Conserve bothmass–energy and relativistic momentum.]59. A woman on a ladder drops small pellets toward apoint target on the floor. (a) Show that, according tothe uncertainty principle, the average distance bywhich she misses the target must be at leastwhere H is the initial height of each pellet abovethe floor and m is the mass of each pellet. Assumethat the spread in impact points is given by x f x i (v x )t. (b) If H 2.00 m and m 0.500 g, whatis x f ?60. Show that the speed of a particle having de Brogliewavelength and Compton wavelength C h/(mc) is61. (a) Find the mass of a solid iron sphere 2.00 cm inradius. (b) Assume that it is at 20°C and has emissivity0.860. Find the power with which it is radiatingelectromagnetic waves. (c) If this sphere were alonein the Universe, at what rate would its temperaturebe changing? (d) Assume Wien’s law describes thesphere. Find the wavelength max of electromagneticradiation it emits most strongly. Although it emits aspectrum of waves having all different wavelengths,model its whole power output as carried by photonsof wavelength max . Find (e) the energy of one photonand (f) the number of photons it emits eachsecond. When the sphere is at thermal equilibriumwith its surroundings, it emits and also absorbs photonsat this rate.ACTIVITIESx f 2 m 1/2 2H g 1/4v 1. Use a black marker or pieces of dark electrical tapeto make a very dark area on the outside of a shoebox.Poke a hole in the center of the dark area with apencil. Now put a lid on the box, and compare theblackness of the hole with the blackness of the surroundingdark area. Based on your observation,explain why the radiation emitted from the hole islike that emitted from a black body.c√1 (/C) 2