课程名称︰近代物理 课程性质︰选修 课程教师︰杨燿州 开课学院：工学院 开课系所︰机械系(所) 考试日期（年月日）︰ 2008.04.10 考试时限（分钟）：三节课 (180分钟) 是否需发放奖励金：是！ 谢谢 （如未明确表示，则不予发放） 试题 : close book, 但是考试前黑板上会有所有需用到的物理常数 Problem 1 [30 points] (a)Find the momemtum (in Mev/c) of an electron whose speed is 0.75c [5%] (b)An observer on a spacecraft moving at 0.800c relative to the earth finds that a car takes 30.0 min to make a trip. How long does the trip take to the driver of the car? [5%] (c)A space craft receding from the earth at 0.75c transmits data at the rate of 5.00*10^3 pulses/s. At what rate are they receiced? [5%] (d)At what speed does the kinetic energy of a particle equal its rest energy? [5%] (e)How much work (in Mev) must be done to increase the speed of an electron from 1.5*10^8 m/s to 2.5*10^8 m/s? [5%] (f)An astronaut is standing in a spacecraft parallel to its direction of motion . An observer on the earth finds that spacecraft speed is 0.5c and the astronaut is 1.5m tall. What is the astronaut's heigh as measured in the spacecraft? [5%] Problem 2 [15 points] (a) The maximum wavelength for photoelectric emmision in tungsten is 230 nm. What wavelength of light must be used in order for electric with a maximum energy of 1.8eV to be ejected? [5%] (b) The distance between adjacent atomic planes in calcite is 0.300nm. Find the smallest angle of Bragg scattering for 0.05-nm x-rays. [5%] (c) There are three chief ways (mechanisms) of photon absorption by a material: the photoelectric effect, the Compton scattering and the pair production. What is the frequency range of photons required for each of the mechanisms? (Answer this question in terms of "visible light", "ultraviolet light", "gamma ray", "X-ray", and so on.) [5%] Problem 4 [20 points] (没有打错 考卷上真的没有第三大题 但不影响总分) (a) Find the kinetic energy of an electron whose de Brolie wave-length is the same as that of a 150-keV x-ray. [5%] (b) Find the phase and group velocities of the de Broglie waves of an electron whose kinetic energy is 400 keV. [5%] (c) A beam of 40-keV electrons is directed at a crystal and diffracted electron are found at an angle of 60(度) relative to the original beam. What is the spacing of the atomic planes of the crystal? A relativistic calculation is need for λ. [5%] (d) Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is λ= hc/ √[KE(KE+2mc^2)] Problem 5 [10 points] The lowest energy possible for a certain particle trapped in a certain box is 1.5 eV. (a) What are the next two higher energies the particle can have? (b) If the particle is an electron, how wide is the box? Problem 6 [15 points] The figure is the schematic of the Compton effect. Please show λ'- λ = λc (1-cosφ) where 1/λ= v/c 1/λ' = v'/c and λc = h/mc (此题会附上课本康普顿效应的图) Problem 7 [10 points] (没有a小题) (b) Find the mass (in GeV/c^2) of a particle whose total energy is 3.00 GeV and whose momentum is 1.2 GeV/c. [5%] (c) Find the total energy of this particle in a reference frame in which its momentum is 1.8 GeV/c. [5%] --

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