課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰李尚凡
開課學院：工學院
開課系所︰機械工程系
考試日期（年月日）︰2008.06.20
考試時限（分鐘）：240
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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 (無法表示)in term of numberk by defineing momentum p of a
particle as an operator, we can get the Schrödininger equation,(無法表示)
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 (無法表示
find(a)the normalization coefficient A (b)the average(expectation)value of r
in the 2s state.
第九題無法表示(1)
2 ▉▉ 2
▉▉▉ ▉ ▉ ▉
▉ ▉▉ ▉▉▉▉ ▉▉
▉▉▉ ▉ ▉ ▉ ▉ ▉▉
▉▉ ▉ ▉ ▉ ▉ ▉
▉ ▉ ▉▉▉ ▉ ▉ ▉ ▉
▉ ▉ ▉ ▉ ▉▉ ▉ ▉
▉▉▉ ▉ ▉ ▉ ▉ ▉ ▉▉
▉ ▉ ▉▉ ▉
▉▉▉▉ ▉
▉▉▉▉▉▉▉▉▉▉▉ ▉▉▉▉▉▉ ▉▉▉▉▉▉▉▉▉
▉▉▉▉
2 2
2 ▉▉▉▉ ▉
▉▉▉▉ ▉▉ ▉ ▉▉ ▉▉ ▉ ▉
▉ ▉ ▉ ▉ ▉ ▉ ▉ ▉▉ ▉ ▉▉▉▉
▉▉ ▉ ▉▉ ▉ ▉ ▉ ▉ ▉
▉ ▉ ▉▉ ▉ ▉ ▉ ▉ ▉▉
▉ ▉ ▉ ▉ ▉ ▉ ▉▉▉ ▉ ▉▉
▉▉▉ ▉ ▉ ▉▉
無法表示(2) 薛丁格方程式的能量表法
10.無法表示
r
▁ ▁
2a
██
█ █
█ r █
█ █ ████
Ψ(r)=A █ █ █ █
█ 2 ▁ █████████ █ █ █
█ █ █ █
█ █ ████
█ █ █
█ a █ ██ ██
█ █ ██
█ █
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※ 編輯: choral 來自: 140.112.250.90 (06/21 14:03)