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）︰ 2008.04.10
考試時限（分鐘）：三節課 (180分鐘)
是否需發放獎勵金：是！ 謝謝
（如未明確表示，則不予發放）
試題 : close book, 但是考試前黑板上會有所有需用到的物理常數
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] (沒有打錯 考卷上真的沒有第三大題 但不影響總分)
(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
(此題會附上課本康普頓效應的圖)
Problem 7 [10 points] (沒有a小題)
(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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