課程名稱︰近代物理 課程性質︰選修 課程教師︰楊燿州 開課學院：工學院 開課系所︰機械系(所) 考試日期（年月日）︰2011/10/25 考試時限（分鐘）：180分鐘 (三節課) 是否需發放獎勵金：是！ （如未明確表示，則不予發放） 試題 : Problem 1 [15 points] The mass of a neutron is 0.94GeV/c^2. (a) How much work must be done to increase the speed of a neutron from 1.5x10^8 m/s to 2.7x10^8 m/s? (b) Find the momentum and total energy of a neutron whose speed is 2.7x10^8 m/s. Problem 2 [15 points] A spacecraft recede from the earth at 0.75c. (a) An observer on earth finds that the spacecraft takes 1 hour to make a trip. How long does the trip take to the astronaut of the spacecraft? (b) If the spacecraft emits a red light with a wavelength of 700nm,what is the corresponding wavelength measured on the earth? (c) The spacecraft takes a trip to a star 15 light-years away. The ast- onaut on the spacecraft sends a signal once a year. How many signals does an observer on earth receive when spacecraft arrives to the star? Problem 3 [10 points] An electron has a de Broglie wavelength of 3.6x10^-12 m. (a) Find its kinetic energy. (b) Find the phase and group velocities. Problem 4 [10 points] A beam of neutrons that emerges from a nuclear reactor contains neutrons with a variety of energies. To obtain neutrons with energy of 0.2eV, the beam is passed thought a crystal whose atomic planes are 0.15nm apart. (a) Find the wavelength of the neutrons. (b) At what angle relative to the original beam will the desired neutrons be diffracted? Problem 5 [10 points] Ultraviolet light of wavelength 310nm and intensity of 1.00W/m^2 is dire- cted at a sodium surface. (a) Find the maximum KE of the photoelectrons. (b) If 0.50 percent of the incident photons produce photoelectrons, how many are emitted per second if the sodium surface has an area of 1.00 cm^2 ? (work function of sodium is 2.4eV) Problem 6 [20 points] A positron with a kinetic energy of 3.000 MeV collides with an electron at rest and the two particles are annihilated. Two photons are produced; one moves in the same direction as the incoming positron and the other moves in the opposite direction. (a) Find the evergies of the photons. (b) Show that pair production cannot occur in empty space. Problem 7 [20 points] The sun's mass is 2x10^30 kg and its radius is 7.0x10^8 m. (a) Derive Gravitational red shift. (b) Find the approximate gravitational red shift in light of wave length 550nm emitted by the sun. --

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