课程名称︰普通物理学甲下 课程性质︰必修 课程教师︰李尚凡 开课学院：工学院 开课系所︰机械工程系 考试日期（年月日）︰2008.06.20 考试时限（分钟）：240 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.write down the Maxwell's equations. Name one significant outcome from these equations and explain your answer briefly, either in Chinese or in English. 2.a mircowave source produces pulses of 20.0-GHz radiation,with each pulse lasting 1.00ns.a parabolic reflector with a face eara of radius 6.00cm is used to focus the microwaves into a parallel beam of radiation,the average power during each pluse is 25.0 kW.(a)what is the wavelength of these microwaves? (b)what is the total energy contained in each pluse?(c)compute the averge energy density inside each pulse.(d)determine the ampitude of the electric and magnetic fields in these microwaves(e)assuming the plused beam strikes an absorbing surface,compute the 1.00-ns duration of each pluse. 3. astronomers observed a 60.0-MHz radio source both directly and by reflection from the sea.if the receiving dish is20.0m above sea level, what is the angel of the radio source above the horizon at first maximum ? 4. A.H.Pfund's method for measuring rhe index of rafraction of glass is illustrated in the figure.one face of aslab of thickness t is pointed white, and a small hole scraped clear at point P serves as a source of diverging rays when the slab is illuminated from below .ray PBB' strikes the clear surface at the critical angel and is totally reflected,as the rays such as PCC'.rays such as PAA' emerge from the clear.on the painted surface there appears a dark circle of diameter d ,surrounded by an illuminated region ,or halo (A)derive an equation for n in terms of the measured quantities d and t.(b) what is the diameter of the dark circle if n=1.52 for the slab 0.6cm thick?(c)if white light is used, the critical angle depends on color caused by dispersion. is the inner edge of the white halo tinged with red light or violet light?explain 5. two wavelength λ and λ+△λ(with △λ<<λ) are incident on a diffraction grating. find the angular separation △θbetween the spectral lines in the mth-order spectrum in terms of λ,△λ,d the slit spacing,and m the order number. 6.for a free relativistic quantum particle moving with speed v , the total energy isE=hf=hω/2π=(ppcc+mmcccc)︿0.5 and the momentum is p=h/λ=hk/2π =γmv for the quantum wave representing the particle,derive the phase speed and the group speed. 7.use the uncertainty principle to show that if an electron were confined inside an atomic uncleus of diameter 2x10︿-15m,it would have to be moving relativistically, while a proton can be moving nonrelativistically. 8. a light source emitting radiation at 7x10︿-14Hz is incapable of ejecting photoelectrons from a certain metal. in an attempt to use this source to ecject photoelectrons from the metal. the source is given a velocity toward the metal. (a)explain how this produre produces photoelectrons.(b)when the speed of the light source is equal to 0.280c,photoelectrons just begin to be ejected from the metal ,what is the work function of the metal?(c)when the speed of the light source is increased to 0.900c,determine the maximum kinetic energy of the photoelectrons. 9. write down one general solution f(x,t)(wave function)to the one-dimensional wave equation (无法表示)in term of numberk by defineing momentum p of a particle as an operator, we can get the Schrödininger equation,(无法表示) put the operator in front of your general solution and show one can get the momentum(with correct sign)of the particle multiplied by the wave function. 10. the wave function for an electron in the 2s state of hydrogen is (无法表示 find(a)the normalization coefficient A (b)the average(expectation)value of r in the 2s state. 第九题无法表示(1) 2 ▉▉ 2 ▉▉▉ ▉ ▉ ▉ ▉ ▉▉ ▉▉▉▉ ▉▉ ▉▉▉ ▉ ▉ ▉ ▉ ▉▉ ▉▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉ ▉▉▉ ▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉ ▉▉ ▉ ▉▉▉▉ ▉ ▉▉▉▉▉▉▉▉▉▉▉ ▉▉▉▉▉▉ ▉▉▉▉▉▉▉▉▉ ▉▉▉▉ 2 2 2 ▉▉▉▉ ▉ ▉▉▉▉ ▉▉ ▉ ▉▉ ▉▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉▉▉▉ ▉▉ ▉ ▉▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉▉ ▉ ▉▉ ▉▉▉ ▉ ▉ ▉▉ 无法表示(2) 薛丁格方程式的能量表法 10.无法表示 r ▁ ▁ 2a ██ █ █ █ r █ █ █ ████ Ψ(r)=A █ █ █ █ █ 2 ▁ █████████ █ █ █ █ █ █ █ █ █ ████ █ █ █ █ a █ ██ ██ █ █ ██ █ █ █ █ ※ 编辑: choral 来自: 140.112.250.90 (06/21 14:03)