Quantum Physics

900 Chapter 27 Quantum Physicsthis region? (b) On the basis of your result in part(a), would you expect to find an electron in a nucleus?Explain.38. After learning about de Broglie’s hypothesis thatparticles of momentum p have wave characteristicswith wavelength h/p, an 80.0-kg student hasgrown concerned about being diffracted when passingthrough a 75.0-cm-wide doorway. Assume thatsignificant diffraction occurs when the width of thediffraction aperture is less than 10.0 times thewavelength of the wave being diffracted. (a) Determinethe maximum speed at which the studentcan pass through the doorway in order to be significantlydiffracted. (b) With that speed, how longwill it take the student to pass through the doorwayif it is 15.0 cm thick? Compare your result withthe currently accepted age of the Universe, which is4.00 10 17 s. (c) Should this student worry aboutbeing diffracted?39. De Broglie postulated that the relationship h/p isvalid for relativistic particles. What is the de Brogliewavelength for a (relativistic) electron whose kineticenergy is 3.00 MeV?40. A monoenergetic beam of electrons is incident on asingle slit of width 0.500 nm. A diffraction pattern isformed on a screen 20.0 cm from the slit. If thedistance between successive minima of the diffractionpattern is 2.10 cm, what is the energy of the incidentelectrons?41. The resolving power of a microscope is proportionalto the wavelength used. A resolution of 1.0 10 11 m (0.010 nm) would be required in orderto “see” an atom. (a) If electrons were used (electronmicroscope), what minimum kinetic energy would berequired of the electrons? (b) If photons were used,what minimum photon energy would be needed toobtain 1.0 10 11 m resolution?45.and is initially known to be within a pond 1.00 mwide. (a) What is the minimum uncertainty in hisspeed? (b) Assuming this uncertainty in speed to prevailfor 5.00 s, determine the uncertainty in Fuzzy’s positionafter this time.Suppose optical radiation ( 5.00 10 7 m) is used to determine the position of anelectron to within the wavelength of the light. Whatwill be the resulting uncertainty in the electron’svelocity?46. (a) Show that the kinetic energy of a nonrelativisticparticle can be written in terms of its momentum asKE p 2 /2m. (b) Use the results of (a) to find theminimum kinetic energy of a proton confined within anucleus having a diameter of 1.0 10 15 m.ADDITIONAL PROBLEMS47. Figure P27.47 shows the spectrum of light emitted by afirefly. Determine the temperature of a blackbody thatwould emit radiation peaked at the same frequency.Based on your result, would you say firefly radiation isblackbody radiation?Relative intensity1.00.80.60.40.2400 500 600Wavelength (nm)Figure P27.47Section 27.7 The Wave FunctionSection 27.8 The Uncertainty Principle42. A 50.0-g ball moves at 30.0 m/s. If its speed is measuredto an accuracy of 0.10%, what is the minimumuncertainty in its position?43. In the ground state of hydrogen, the uncertaintyin the position of the electron is roughly 0.10 nm.If the speed of the electron is on the order of theuncertainty in its speed, how fast is the electronmoving?44. Suppose Fuzzy, a quantum mechanical duck, lives in aworld in which h 2 J s. Fuzzy has a mass of 2.00 kg48. An x-ray tube is operated at 50 000 V. (a) Find the minimumwavelength of the radiation emitted by this tube.(b) If the radiation is directed at a crystal, the firstordermaximum in the reflected radiation occurswhen the grazing angle is 2.5°. What is the spacingbetween reflecting planes in the crystal?49. The spacing between planes of nickel atoms in anickel crystal is 0.352 nm. At what angle does a secondorderBragg reflection occur in nickel for 11.3-keVx-rays?50. Johnny Jumper’s favorite trick is to step out of his16th-story window and fall 50.0 m into a pool. Anews reporter takes a picture of 75.0-kg Johnnyjust before he makes a splash, using an exposure