Quantum Physics

Problems 89917. When light of wavelength 254 nm falls on cesium,the required stopping potential is 3.00 V. If light ofwavelength 436 nm is used, the stopping potentialis 0.900 V. Use this information to plot a graph likethat shown in Figure 27.6, and from the graph determinethe cutoff frequency for cesium and its workfunction.18. Ultraviolet light is incident normally on the surface ofa certain substance. The binding energy of theelectrons in this substance is 3.44 eV. The incidentlight has an intensity of 0.055 W/m 2 . The electronsare photoelectrically emitted with a maximum speed of4.2 10 5 m/s. How many electrons are emitted froma square centimeter of the surface each second?Assume that the absorption of every photon ejects anelectron.Section 27.3 X-Rays19. The extremes of the x-ray portion of the electromagneticspectrum range from approximately 1.0 10 8m to 1.0 10 13 m. Find the minimum acceleratingvoltages required to produce wavelengths at thesetwo extremes.20. Calculate the minimum-wavelength x-ray that can beproduced when a target is struck by an electron thathas been accelerated through a potential difference of(a) 15.0 kV and (b) 100 kV.21. What minimum accelerating voltage would berequired to produce an x-ray with a wavelength of0.030 0 nm?Section 27.4 Diffraction of X-Rays byCrystals22. A monochromatic x-ray beam is incident on a NaClcrystal surface with d 0.353 nm. The second-ordermaximum in the reflected beam is found when theangle between the incident beam and the surface is20.5°. Determine the wavelength of the x-rays.23. Potassium iodide has an interplanar spacing ofd 0.296 nm. A monochromatic x-ray beam shows afirst-order diffraction maximum when the grazingangle is 7.6°. Calculate the x-ray wavelength.24. The spacing between certain planes in a crystal isknown to be 0.30 nm. Find the smallest angle of incidenceat which constructive interference will occur forwavelength 0.070 nm.25. X-rays of wavelength 0.140 nm are reflected from a certaincrystal, and the first-order maximum occurs at anangle of 14.4°. What value does this give for the interplanarspacing of the crystal?Section 27.5 The Compton Effect26. X-rays are scattered from electrons in a carbon target.The measured wavelength shift is 1.50 10 3 nm.Calculate the scattering angle.27. Calculate the energy and momentum of a photon ofwavelength 700 nm.28. A beam of 0.68-nm photons undergoes Compton scatteringfrom free electrons. What are the energy andmomentum of the photons that emerge at a 45° anglewith respect to the incident beam?29. A 0.001 6-nm photon scatters from a free electron. Forwhat (photon) scattering angle will the recoiling electronand scattered photon have the same kineticenergy?30. X-rays with an energy of 300 keV undergo Comptonscattering from a target. If the scattered rays aredeflected at 37.0° relative to the direction of theincident rays, find (a) the Compton shift at this angle,(b) the energy of the scattered x-ray, and (c) the kineticenergy of the recoiling electron.31.A 0.110-nm photon collides with astationary electron. After the collision, theelectron moves forward and the photon recoils backwards.Find the momentum and kinetic energy of theelectron.32. After a 0.800-nm x-ray photon scatters from a freeelectron, the electron recoils with a speed equal to1.40 10 6 m/s. (a) What was the Compton shiftin the photon’s wavelength? (b) Through what anglewas the photon scattered?33. A 0.45-nm x-ray photon is deflected through a 23°angle after scattering from a free electron. (a) What isthe kinetic energy of the recoiling electron? (b) Whatis its speed?Section 27.6 The Dual Nature of Light and Matter34. Calculate the de Broglie wavelength of a proton movingat (a) 2.00 10 4 m/s; (b) 2.00 10 7 m/s.35.(a) If the wavelength of an electron is 5.00 10 7 m,how fast is it moving? (b) If the electron has a speed of1.00 10 7 m/s, what is its wavelength?36. A 0.200-kg ball is released from rest at the top of a50.0-m tall building. Find the de Broglie wavelength ofthe ball just before it strikes the Earth.37. The nucleus of an atom is on the order of 10 14 min diameter. For an electron to be confined to anucleus, its de Broglie wavelength would have to be ofthat order of magnitude or smaller. (a) What wouldbe the kinetic energy of an electron confined to