Download PHYSICS TEST

PHYSICS TEST
Time–170 minutes
100 Questions
Directions: Each of the questions or incomplete statements below is followed by five suggested
answers or completions. Select the one that is best in each case and then blacken the
corresponding space on the answer sheet.
1. A rock is thrown vertically upward with initial speed v0. Assume a friction force proportional to
–v, where v is the velocity of the rock, and neglect the buoyant force exerted by air. Which of the
following is correct?
(A) The acceleration of the rock is always equal to g.
(B) The acceleration of the rock is equal to g only at the top of the flight.
(C) The acceleration of the rock is always less than g.
(D) The speed of the rock upon return to its starting point is v0.
(E) The rock can attain a terminal speed greater than v0 before it returns to its starting point.
解：在顶点，石块的速度为零，此时空气摩擦力为零，故加速度为 g，选(B)。对于选项(E)，
石块有可能获的收尾速度，但由于有阻力，必小于 v0。
2. A satellite orbits the Earth in a circular orbit. An astronaut on board perturbs the orbit slightly
by briefly firing a control jet aimed toward the Earth’s center. Afterward, which of the following is
true of the satellite’s path?
(A) It is a ellipse.
(B) It is a hyperbola.
(C) It is a circle with larger radius.
(D) It is a spiral with increasing radius.
(E) It exhibits many radial oscillations per revolution.
3. For blue light, a transparent material has a relative permittivity (dielectric constant) of 2.1 and a
relative permeability of 1.0. If the speed of light in a vacuum is c, the phase velocity of blue light
in an unbounded medium of this material is
(A)
3.1c
(B)
2.1c
(C)
c
1.1
(D)
c
2 .1
(E)
c
3 .1
4. The equation y  A sin 2 (
t x
 ) , where A, T, and  are positive constants, represents a
T 
wave whose
(A) amplitude is 2A
(B) velocity is in the negative x-direction
(C) period is
T

x
(D) speed is
t

(E) speed is
T


A
M
h0
B
3M
5. Two small spheres of putty, A and B, of mass M and 3M, respectively, hang from the ceiling on
strings of equal length l. Sphere A is drawn aside so that it is raised to a height h0 as shown above
and then released. Sphere A collides with sphere B, they stick together and swing to a maximum
height h equal to
(A)
(B)
(C)
(D)
(E)
1
h0
16
1
h0
8
1
h0
4
1
h0
3
1
h0
2
O
x
Track
y
6. A particle is initially at rest at the top of a curved frictionless track. The x- and y-coordinates of
the track are related in dimensionless units by y 
x2
, where the positive y-axis is in the
4
vertical downward direction. As the article slides down the track, what is its tangential
acceleration?
(A) 0
(B) g
(C)
(D)
(E)
gx
2
gx
x2  4
gx 2
x 2  16

F = 10 N
2 kg
7. A 2-kilogrom box hangs by a massless rope from a ceiling. a force slowly pulls the box
horizontally to the side until the horizontal force is 10 newtons. The box is then equilibrium as
shown above. The angle that the rope makes with the vertical is closest to
(A) arctan 0.5
(B) arcsin 0.5
(C) arctan 2.0
(D) arcsin 2.0
(E) 45
8. A 5-kilogram stone is dropped on a nail and drives the nail 0.025 meter into a piece of wood. If
the stone is moving at 10 meters per second when it hits the nail, the average force exerted into the
wood is most nearly
(A) 10 N
(B) 100 N
(C) 1000 N
(D) 10,000 N
(E) 100,000 N
9. A wire of diameter 0.02 meter contains 11028 free electrons per cubic meter. For an electric
current of 100 amperes, the drift velocity of electrons in the wire is most nearly
(A)
(B)
(C)
(D)
(E)
0.61029 m/s
11019 m/s
51010 m/s
2104 m/s
8103 m/s
Electric Field
Magnitude
A
B
C
A, B, C, D, E
D
E
O
R
r
10. A isolated sphere of radius R contains a uniform volume distribution of positive charge. Which
of the curves on the graph above correctly illustrates the dependence of the magnitude of the
electric field of the sphere as function of the distance r from its center?
(A) A
(B) B
(C) C
(D) D
(E) E
  J?
11. Which of the following equations is a consequence of the equation   H  D
  J)  0
(A)   (D
  J)  0
(B)   (D
  J)  0
(C) (D
 J 0
(D) D
 J  0
(E) D
12. A source of 1-kilohertz sound is moving straight toward you at a speed 0.9 times the speed on
sound. The frequency you receive is
(A) 0.1 kHz
(B) 0.5 kHz
(C) 1.1 kHz
(D) 1.9 kHz
(E) 10 kHz
13. Two coherent sources of visible monochromatic light form an interference pattern on a screen.
If the relative phase of the sources is varied from 0 to 2 at a frequency of 500 hertz, which of the
following best describes the effect, if any, on the interference pattern?
(A) It is unaffected because the frequency of the phase change is very small compared to the
frequency of visible light.
(B) It is unaffected because the frequency of the phase change is an integral multiple of .
(C) It is destroyed except when the phase difference is 0 or .
(D) It is destroyed for all phase differences because the monochromaticity of the sources is
destroyed.
(E) It is not destroyed but simply shifts positions at a rate too rapid to be detected by the eye.
14. For an ideal gas, the specific heat at constant pressure Cp is greater than the specific heat at
constant volume Cv because the
(A) gas does work on its environment when its pressure remains constant while its temperature is
increased
(B) heat input per degree increase in temperature is the same in processes for which either the
pressure or the volume is kept constant
(C) pressure of the gas remains constant when its temperature remains constant
(D) increase in the gas’s internal energy is greater when the pressure remains constant than when
the volume remains constant
(E) heat needed is greater when the volume remains constant than when the pressure remains
constant
15. A sample of N atoms of helium gas is confined in a 1.0 cubic meter volume. The probability
that none of the helium atoms is in a 1.010–6 cubic meter volume of the container is
(A) 0
(B) (10–6)N
(C) (1–10–6)N
(D) 1–(10–6)N
(E) 1
16. Except for mass, the properties of the muon most closely resemble the properties of the
(A) electron
(B) graviton
(C) photon
(D) pion
(E) proton
17. Suppose that
A
Z
X decays by natural radioactivity in two stages to
A 4
Z 1
Y . The two stages
would most likely be which of the following?
First Stage
Second Stage
(A)
(B)
(C)
(D)
– emission with an antineutrino  emission
– emission
 emission with a neutrino
–
 emission
 emission
Emission of a deuteron
Emission of two neutrons
(E)  emission
 emission
18. The wave function  ( x)  A exp{ 
b2 x2
} , where A and b are real constants, is a
2
normalized eigenfunction of the Schrödinger equation for a particle of mass M and energy E in a
one dimensional potential V(x) such that V(x) = 0 at x = 0. Which of the following is correct?
(A) V 
 2b 4
2M
(B) V 
 2b 4 x 2
2M
 2b 6 x 4
(C) V 
2M

(D) E   b 1  b x
2
(E) E 
2
2
2

 2b 4
2M
19. The energy levels of the hydrogen atom are given in terms of the principal quantum number n
and a positive constant A by the expression
1
2
(A) A(n  )
(B) A(1–n2)
(C) A( 
1 1
 )
4 n2
(D) An2
(E) 
A
n2
20. A positive kaon (K+) has a rest mass of 494MeV/c2, whereas a proton has a rest mass of
938MeV/c2. If a kaon has a total energy that is equal to the proton rest energy, the speed of the
kaon is most nearly
(A) 0.25c
(B) 0.40c
(C) 0.55c
(D) 0.70c
(E) 0.85c
21. Two observers O and O’ observe two events a and B. the observers have a constant relative
speed of 0.8c. In units such that the speed of light is 1, observer O obtained the following
coordinates:
Event A: x=3, y=3, z=3, t=3
Event B: x=5, y=3, z=1, t=5
What is the length of the space-time interval between these two events, as measured by O’?
(A) 1
(B)
2
(C) 2
(D) 3
(E) 2 3
解：由狭义相对论，事件的时空距离
S 2  x 2  y 2  z 2  c 2 t 2
为守恒量，与参考系无关。所以只需要在 O 的参考系中计算即可。答案选(C)。
22. Which of the following statements most accurately describes how an electroomagnetic field
behaves under a Lorentz transformation?
(A) The electric field transforms completely into a magnetic field.
(B) If initially there is only an electric field, after the transformation there may be both an electric
and a magnetic field.
(C) The electric field is unaltered.
(D) The magnetic field is unaltered.
(E) It cannot be determined unless a gauge transformation is also specified.
解：在相对论下，电磁场被完全统一起来。电磁势和 A 是同一四维矢量的不同分量，
 i
A  ( A,  ) ，
c
在不同参考系间变换时，可相互转换。选（B）
。
23. Which of the following statements concerning the electrical conductivities at room
temperature of a pure copper sample and a pure silicon sample is NOT true?
(A) The conductivity of the copper sample is many orders of magnitude greater than that of the
silicon sample.
(B) If the temperature of the copper sample is increased, its conductivity will decrease.
(C) If the temperature of the silicon sample is increased, its conductivity will increase.
(D) The addition of an impurity in the copper sample always decreases its conductivity.
(E) The addition of an impurity in the silicon sample always decreases its conductivity.
解：对于导体（本题中为铅）
，随着温度上升电子与离子实的碰撞逐渐剧烈，电子自由程下
降，导电性能降低；对于本征半导体(本题中为硅）
，温度上升使载流子浓度上升，导电能力
升高。而掺杂（施主或受主）往往能使半导体的导电性大大增加。选（E）
。
R
+
G
- +
100 V, 1 
24. The battery in the diagram above is to be charged by the generator G. The generator has a
terminal voltage of 120 volts and when the charging current is 10 amperes. The battery has a emf
of 100 volts and an internal resistance of 1 ohm. In order to charge the battery at 10 amperes
charging current, thee resistance R should be set at
(A)
(B)
(C)
(D)
(E)
0.1 
0.5 
1.0 
5.0 
10.0 
解：注意电池与发电机 G 反接，所以 R 
120  100
 1  1.0() ，选（C）。
10
25. A charged particle is released from rest in a region where there is a constant electric field and a
constant magnetic field. If the two fields are parallel to each other, the path of the particle is a
(A) circle
(B) parabola
(C) helix
(D) cycloid
(E) straight line



解：带电体又静止释放，初始受力沿电场方向，使得 v // E ，从而也平行于磁场 B 。由洛



伦兹力公式， F  q (v  B ) ，不受磁场力作用，只受电场作用，直线运动。选（E）
。
26. A nickel target (Z=28) is bombarded with fast electrons. The minimum electron kinetic energy
needed to produce x-rays in the K series is most nearly
(A) 10 eV
(B) 100 eV
(C) 1000 eV
(D) 10,000 eV
(E) 100,000 eV
解：考场上作为估算，对于 K 线系，可用氢原子能级公式估算，
e 4 Z 2
Z2
E
 13.6 2 eV 。
2 n 2
n
取 Z=28 ， n=1 ， 约 为 10,000eV 。 选 （ D ）。 严 格 计 算 可 用 莫 塞 莱 公 式 ：
v K  0.248  1016 (Z  b) 2
b ~1 。
27. The hypothesis that an electron possesses spin is qualitatively significant for the expanation of
all of the following topics EXCEPT the
(A) structure of the periodic table
(B) specific heat of metals
(C) anomalous Zeeman effect
(D) deflection of a moving electron by a uniform magnetic field
(E) fine structure of atomic spectra
解：
（D）涉及的内容为普物甚至是高中课程，显然不需要考虑自旋就可解释。选(D)。
（B）
比较容易混，关键是自旋的引入使态的数目加倍。
28. Eigenfunctions for a rigid dumbbell rotating about its center have a jjj dependence of the form
    Ae im , where m is a constant. Which of the following values of A will properly
normalize the eigenfunction?
(A)
2m
(B) 2
(C) (2)2
(D)
(E)
1
2
1
2
解：最简单的量子力学题。令
2
2

im
im
2
  d   Ae Ae d  A 2  1,
0
答案选(D)。
0
A
1
2
。
29. A negative test charge is moving near a long straight wire in which there is a current. A force
will act on the test charge in a direction parallel to the direction of the current if the motion of the
charge is in a direction
(A) toward the wire
(B) away from the wire
(C) the same as that of the current
(D) opposite to that of the current
(E) perpendicular to both the direction of the current and the direction toward the wire



解：磁场方向环绕电流，服从右手定则。由洛伦兹力公式， F  q (v  B ) 。本题关键是注



意到电量为负， F   q (v  B) ，故答案选（A）
。
30. The configuration of the potassium atom in its ground state is 1s22s22p63s23p64s1. Which of
the following statements about potassium is true?
(A) Its n=3 shell is completely filled.
(B) Its 4s subshell is completely filled.
(C) Its least tightly bound electron has l=4.
(D) Its atomic number is 17.
(E) Its electron charge distribution is spherically symmetrical.
解：
（A）不对，还有 3d 轨道；(B)不对，还差一个才满；(C)不对，最外层电子 n=4,角动量
由 s 表示为 l=0；
（D）不对，显然为 19。答案选（E）
，因为 s 轨道为球对称，而 p 轨道虽不
球对称，但由于被全部占满，所以电荷分布仍为球对称。
Monochromatic
Light Source of
Frequency 
A
Photocathode
Collector
D. C. Power
Supply
Question 31-33 refer to the following apparatus used to study the photoelectric effect.
In this apparatus, the photocathode and the collector are made from the same material. The
potential V of the collector, measured relative to ground, initially zero and is then increased or
decreased monotonically. The effect is described by Einstein's photoelectric equation
eV  h  W
31. When the photoelectric equation is satisfied and applicable to this situation, V is the
(A) negative value at which the current stops
(B) negative value at which the current starts
(C) positive value at which the current stops
(D) positive value at which the current starts
(E) voltage induced when the light is on
解：收集极加负电压，排斥电子。只有能量足够高的电子才能被收集。光电子出射方向各异，
水平出射最易达到收集极。当收集极恰好接收不到电子时，说明|eV|是出射光电子的最大动
能。答案选（A）
。
32. The photoelectric equation is derived under the assumption that
(A) electrons are restricted to orbits of angular momentum n , where n is an integer
(B) electrons are associated with waves of wavelength   h / p , where p is momentum
(C) light is emitted only when electrons jump between orbits
(D) light is absorbed in quanta of energy E  h
(E) light behaves like a wave
解：熟知的常识。答案选（D）
。
33. The quantity W in the photoelectric equation is the
(A) energy difference between the two lowest electron orbits in the atoms of the photocathode
(B) total light energy absorbed by the photocathode during the measurement
(C) minimum energy a photon must have in order to be absorbed by the photocathode
(D) minimum energy required to free an electron from its binding to the cathode material
(E) average energy of all electrons in the photocathode
解：W 表示脱出功，答案选（D）
。
Question 34-36
The potential energy of a body constrained to move on a straight line is kx4, where k is a constant.
The position of the body is x, its speed v, its linear momentum p, and its mass m.
34. The force on the body is
(A)
1
mv 2
2
(B) –4kx3
(C) kx4
(D) 
kx5
5
(E) mg
解：直接对势能求导，得 F  
dU
 4kx3 。答案选(B)。其实从量纲上看，（A）、（C）
dx
为能量，
（D）为能量乘上距离，均不是力的单位。
35. The Hamiltonian function for this system is
(A)
p2
 kx4
2m
(B)
p2
 kx 4
2m
(C) kx4
1 2
mv  kx 4
2
1
mv 2
(E)
2
(D)
解：对于变换方程不显含 t 的有势力系（这一条件在 Sub 考试中，几乎必然满足）
，H=T+V。
答案选（A）
。
36. The body moves from x1 at time t1 to x2 at time t2. Which of the following quantities is an
extremum for the x–t curve corresponding to this motion, if end points are fixed?
1 2
4
 mv  kx dt
2

(A)

t2
(B)

t2
(C)
 mxvdt
t1
t1
1
2
 mv dt
2


t2
t1
x2
1 2
4
 mv  kx dx
2

(D)

(E)
 mvdx
x1
x2
x1
解：本题涉及分析力学的变分原理部分，一般比较生疏。由哈密顿原理，定义哈密顿作用量
t2
S   Ldt ，
t1
则真实运动使 S 取极值。其中 L 为拉格朗日量，L=TV。答案选（A）
。


r

m
37. The figure above represents a point mass m attached to the ceiling b a cord of fixed length l. If
the point mass moves in a horizontal circle of radius r with uniform angular velocity , the tension
in the cord is
r
l
(A) mg  
 

2
(B) mg cos
(C)
mr
 
sin  
2

2

4
(D) m  r  g
2
(E) m  r  g
2

1
2 2

1
2 2
F cos  / 2  mg ，
解：由竖直方向受力平衡
得
F
mg
mgl
。

cos / 2
l2  r2
从另一个角度 F 等于重力和离心力合力


1
F  m  4r 2  g 2 2 。
答案选（E）
。
无妨，38 缺图。
38. If logical 0 is 0 volts and logical 1 is +1 volt, the circuit shown above is a logic circuit
commonly known as
(A) an OR gate
(B) an AND gate
(C) a 2-bit adder
(D) a flip-flop
(E) a fanout
解：真值表如下
input1
input2
output
0
0
0
1
0
1
0
1
1
1
1
1
或门。答案选（A）
。
103
Gain
102
10
1
103
104
105
106
 (s -1)
39. The gain of an amplifier is plotted versus angular frequency  in the diagram above. If K and
a are positive constants, the frequency dependence of the gain near =310–5 second–1 is most
accurately expressed by
(A) Ke
 a
(B) K
2
(C) K
(D) K
1
(E) K
2
解：在=3105second-1 处，约为斜率为-2 的直线。注意到此图为双对数曲线，所以
ln g a i n 2 ln   c ，
g a i n e c 2  k 2 。
答案选(E)。
40. An experimenter measures 9934 counts during one hour from a radioactive sample. From this
number the counting rate of the sample can be estimated with a standard deviation of most nearly
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
41. Which of the following nuclei has the largest binding energy per nucleon? (Consider the most
abundant isotope of each element.)
(A) Helium
(B) Carbon
(C) Iron
(D) Uranium
(E) Plutonium
解：核子的平均结合能和原子序数 Z 的关系是：两头小，中间大，在 Z=55 左右达到极值。
由此大家可以思考一下为什么为获取能量，Z 小时为核聚变，Z 大时为核裂变。铁的原子序
数 Z=56，平均结合能最大。答案选（C）
。不要误以为铀是核燃料就选择（D）
。
42. A proton beam is incident on a scatterer 0.1 centimeter thick. The scatterer contains 1020 target
nuclei per cubic centimeter. In passing through the scatterer, one proton per incident million is
scattered. The scattering cross section is
(A) 10–29 cm2
(B) 10–27 cm2
(C) 10–25 cm2
(D) 10–23 cm2
(E) 10–21 cm2
解：散射几率 P=1/106，为无量纲量。散射截面的量纲为米 2，靶核浓度 n 量纲为米-3，厚
度 l 量纲为米。所以为凑得一个无量纲数，显然公式为 P  n  l   （其实公式本身很简单，
这里只是举一个量纲分析的例子，不一定很恰当。由于 P 为无量纲数，似乎 P 可以等于
(n  l   ) n ，这时需要用物理思想去判断 n 的取值）。答案选（C）。
A
m
k
B
2m
k
C
m
43. Three masses are connected by two springs as shown above. A longitudinal normal mode with
frequency
1
2
k
is exhibited by
m
(A) A, B, C all moving in the same direction with equal amplitude
(B) A and C moving in opposite directions with equal amplitude, and B at rest
(C) A and C moving in the same direction with equal amplitude, and B moving in the opposite
direction with the same amplitude
(D) A and C moving in the same direction with equal amplitude, and B moving in the opposite
direction with twice the amplitude
(E) none of the above
解：首先(B)所属情况是可实现的，A、C 对 B 的作用力始终大小相等方向相反，B 保持静
止。A、C 与普通弹簧振子完全相等。答案选（B）
。
44. A uniform stick of length L and mass M lies on a frictionless horizontal surface. A point
particle of mass m approaches the stick with speed v an a straight line perpendicular to the stick
that intersects the stick at one end, as shown above. After the collision, which is elastic, the
particle is at rest. The speed V of the center of mass of the stick after the collision is
m
v
M
m
v
(B)
M m
(A)
(C)
m
v
M
(D)
m
v
M m
(E)
3m
v
M
解：由动量守恒，碰撞后杆的动量为 mv。由于质点组相对质心动量为零，所以质点组的动
量等于质心速度乘以总质量。 mv  ( M  m) , Vc 
m
v 。答案选（B）。
M m
45. Photons of wavelength  scatter elastically on free protons initially at rest. The wavelength of
the photons scattered at 90 is increased by
(A) /137
(B) /1836
(C) h/mec, where h is Planck’s constant, me the rest mass of an electron, and c the speed of light
(D) h/mpc, where h is Planck’s constant, mp the rest mass of an proton, and c the speed of light
(E) zero
解：可以看作广义的 Compton 散射，
 ' 
h
(1  cos ) ，
mc
m 为散射物的静止质量。对于本题， = 900，
 ' 
h
，
mpc
答案选（D）
。请牢记 Compton 散射实验及公式，否则后果自负。
46. A blackbody at temperature T1 radiates energy at a power level of 10 milliwatts (mW). The
same blackbody, when at a temperature 2T1, radiates energy at a power level of
(A) 10 mW
(B) 20 mW
(C) 40 mW
(D) 80 mW
(E) 160 mW
解：由斯特藩定律，黑体的总辐射能力和它的绝对温度的四次方成正比，
P  T 4 。
答案选（E）
。
47. The Franck-Hertz experiment and related scattering experiments show that
(A) electrons are always scattered elastically from atoms
(B) electrons are never scattered elastically from atoms
(C) electrons of a certain energy range can be scattered in elastically, and the energy lost by
electrons is discrete
(D) electrons always lose the same energy when they are scattered inelastically
(E) there is no energy range in which the energy lost by electrons varies continuously
解：即使不知道 Franck-Hertz 试验的具体内容，也可发现选项中只有（C）的叙述是正确的。
（A）
、(B)、(D)显然不对；
（E）选项，当电子能量较低时，无法触及原子内部，此时为连
续散射谱。
48. A transition in which one photon is radiated by the electron in a hydrogen atom when the
electron’s wave function changes from 1 to 2 is forbidden if 1 and 2
(A) have opposite parity
(B) are orthogonal to each other
(C) are zero at the center of the atomic nucleus
(D) are both spherically symmetrical
(E) are associated with different angular momenta
解：由1 和2 为球对称可知，二者角量子数均为 l=0。而跃迁选择定则要求跃迁前后 l= 1，
所以无法跃迁。答案选（D）
。
49. The Hamiltonian operator in the Schrödinger equation can be formed from the classical
Hamiltonian by substituting
(A) wavelength and frequency for momentum and energy
(B) a differential operator for momentum
(C) transition probability for potential energy
(D) sums over discrete eigenvalues for integrals over continuous variables
(E) Gaussian distributions of observables for exact values
p2
解：只需做如下变换： p  i,
  2  2 。答案选（B）。
2m
50. The Hall effect is used in solid-state physics to measure
(A) ratio of charge to mass
(B)
(C)
(D)
(E)
magnetic susceptibility
the sign of the charge carriers
the width of the gap between the conduction and valence bands
Fermi energy
解：霍尔系数 R H 
1
，n 为载流子浓度，q 为载流子电量。当载流子带负电时，霍尔系数
nq
为负；相反则为正。答案选（C）
。此外霍尔系数显然还可用来测量载流子浓度。
51. One feature common to both the Debye theory and the Einstein theory of the specific heat of a
crystal composed of N identical atoms is that the
(A) average energy of each atom is 3kT
(B) vibrational energy of the crystal is equivalent to the energy of 3N
(C) crystal is assumed to be continuous for all elastic waves
(D) speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves
(E) upper cutoff frequency of the elastic waves is the same
解：Einstein 和 Debye 模型的共同点是：晶格振动等效为 3N 个谐振子（因为自由度为 3N）
；
不同点是：Einstein 很粗糙的假设所有谐振子频率相同，Debye 假设从 0 增大到一个截至
频率D。答案选（B）
。
52. A cube has a constant electric potential V on its surface. If there are no charges inside the cube,
the potential at the center of the cube is
(A) zero
(B) V/8
(C) V/6
(D) V/2
(E) V
解：立方体内无电荷，没有电力线，电势相等。答案选(E)。
53. A charged particle oscillates harmonically along the x-axis as shown above. The radiation from
the particle is detected at a distant point P, which lies in the xy-plane. The electric field at P is in
the
(A) z direction and has a maximum amplitude at =90
(B) z direction and has a minimum amplitude at =90
(C) xy-plane and has a maximum amplitude at =90
(D) xy-plane and has a minimum amplitude at =90
(E) xy-plane and has a maximum amplitude at =45
解：
54. A dielectric of dielectric constant K is placed in contact with a conductor having surface
charge density , as shown above. What is the polarization (bound) charge density p on the
surface of the dielectric at the interface between the two materials?
(A) 
K
1 K
K
1 K
(C) K
1 K
(D) 
K
1 K
(E) 
K
(B) 
解： 由边界条件

 
n  ( D2  D1 )   ，

由于导体内部电场为零， D1  0 。所以介质内部
D2n  
而




D2   0 E2  P  K 0 E2

 
 
 K 1
P2 n  n  P2 n  n  ( D2   0 E 2 )    

K
K
所以束缚电荷密度
 P   P2 n 
1 K

K
答案选（E）
。
55. The mean kinetic energy of electrons in metals at room temperature is usually many times the
thermal energy kT. Which of the following can best be used to explain this fact?
(A) the energy-time uncertainty relation
(B) The Pauli exclusion principle
(C) The degeneracy of the energy levels
(D) The Born approximation
(E) The wave particle duality
解：Pauli 不相容原理限制一个能级上可允许的电子数目，从而迫使电子向更高能级上排布。
使平均动能往往远大于 kT。答案选（B）
。
56. If  is a normalized solution of the Schrödinger equation and Q is the operator corresponding
to a physical observerble x, the quantity *Q may be integrated to obtain the
(A) normalization constant for 
(B) special overlap of Q with 
(C) mean value of x
(D) uncertainty in x
(E) time derivative of x
 ˆ
d ，其中 Â 为 A 对应的算符。答
解：量子力学中，可观测力学量 A 的平均值 A   A

案选（C）
。
57. Which of the following is an eigenfunction of the linear momentum operator  i

with a
x
positive eigenvalue k ; i.e., an eigenfuntion that describes a particle that is moving in free space
in the direction of positive x with a precise linear momentum?
(A) cos kx
(B) sin kx
(C) e
(D) e
(E) e
 ikx
ikx
 kx
解：自由粒子本征态为量子力学基础知识，答案选（D）。若不敢肯定，可以现场求导。
 i
 ikx
e  i  ikeikx  keikx 。
x
58. In an ordinary hologram, coherent monochromatic light produces a 3-dimentional picture
because wave information is recorded for which of the following?
I. Amplitude
II. Phase
III. Wave-front angular frequency
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
解：所谓全息照相，指记录下全部信息，包括波前的相位和振幅（实际为振幅强度的相对分
布）
。答案选（B）
。

59. The dispersion law for a certain type of wave motion is   c k  m
2
2

1
2 2
, where  is the
angular frequency, k is the magnitude of the propagation vector, and c and m are constants. The
group velocity of these waves approaches
(A)
(B)
(C)
(D)
(E)
infinity as k0 and zero as k
infinity as k0 and c as k
c as k0 and zero as k
zero as k0 and infinity as k
zero as k0 and c as k
解：由群速度公式 v g 
vg 
d

dk
d
，本题中
dk
c2k
c2k 2  m2
，
k时， v g  c 。所以答案选（E）。请再牢记一下相速的公式 v p 

k
。
60. A particle of mass m that move s along the x-axis has potential energy V(x)=a+bx2，where a
and b are positive constants. Its initial velocity is v0 at x=0. It will execute simple harmonic
motion with a frequency determined by the value of
(A) b alone
(B) b and a alone
(C) b and m alone
(D) b, a, and m alone
(E) b, a, m, and v0
解：由一维谐振子公式，  
2b
。答案选（C）
。显然与 a 无关，因为势能的零点选取
m
由任意性，或者说质点受力 F  
dV
 2bx 与 a 无关。
dx
Questions 61-62
The equation of motion of a rocket in free space can be written
m
dv
dm
u
0
dt
dt
where m is the rocket’s mass, v is its velocity, t is time, and u is a constant.
61. The constant u represents the speed of the
(A) rocket at t=0
(B) rocket after its fuel spent
(C) rocket in its instantaneous rest frame
(D) rocket’s exhaust in a stationary frame
(E) rocket’s exhaust relative to the rocket
解：由动量守恒
m  dmv  mv  dv  Vdm
mdv  V  vdm  0 ，
则
m
dv
dm
u
0
dt
dt
其中 V 为燃料被抛出后的速度。
令 u  V  v ，为燃料的相对抛出速度。
（*）
答案选(E)。
62. The equation can be solved to give b as a function of m. If the rocket has m=m0 and v=0 when
it starts, what is the solution?
(A) um0 / m
(B) u exp m0 / m
(C) u sin m0 / m
(D) u tan m0 / m
(E) None of the above.
解：由（*）式得
dm
dv

m
u
两边积分得
mt   m0 e

v t  v0
u
所以
vt   v0  u ln
m0
m
 u ln 0
mt 
mt 
答案选（E）
。
63. A point charge –q coulombs is placed at a distance d from a large grounded conducting plane.
The surface charge density on the plane a distance D from the point charge is
(A)
q
4D
(B)
qD 2
2
qd
查
2D 3
qd
(D)
2D 4
(C)
(E)
qd
4 0 D 2
解：因为导体板电势为 0，用镜像法。在-d 放置一镜电荷+q，易得在 D 处
E  2
q
4 0 D
由边界条件


n  ( E 2  E1 ) 
0
并考虑到导体内部电场为 0，
 
答案选（C）
。
qd
2D 3
2

d
qd

D 2 0 D 3
64. An alternating current electrical generator has a fixed internal impedance Rg+jXg and is used
to supply power to a passive load that has a impedance Rg+jXl, where j 
 1 , R g  0 , and
X g  0 . For maximum power transfer between the generator and the load, Xl should be equal to
(A) 0
(B) Xg
(C) –Xg
(D) Rg
(E) –Rg
解：
65. A current i in a circular loop of radius b produces a magnetic field. At a fixed point far from
the loop, the strength of the magnetic field is proportional to which of the following combinations
of i and b?
(A) ib
(B) ib2
(C) i2b
i
b
i
(E) 2
b
(D)
解：取特殊一点的点，计算环轴线上距中心距离为 L 处的磁感应强度 B。
 
B 0
4
 
Idl  rˆ  0 i 2b
 r 2  4 L2  b 2
b
L2  b 2

 0i
2
b2
L
2
 b2

3
2
当 L>>b 时， B  ib 。答案选（B）
。
2
66. For a system in which the number of particles is fixed, the recirocal of the Kelvin temperature
T is given by which of the following derivatives? (Let P=pressure, V=volume, S=entropy, and
U=internal energy.)
 P 

 V  S
(A) 
 P 

 S V
(B) 
 S 

 P U
(C) 
 V 

 P U
(D) 
 S 

 U V
(E) 
解：由热力学基本方程
dU  TdS  pdV 。
把 U 作为 S、V 的函数 U = U(S,V),全微分为
 U 
 U 
dU  
 dS  
 dV 。
 S V
 V  S
比较以上两式
1  S 


T  U V
答案选（E）
。
67. A large isolated system of N weakly interacting particles is in thermal equilibrium. Each
particle has only 3 possible nondegenerate states of energies 0, , and 3. When the system is at an
absolute temperature T>>/k, where k is Boltzmann’s constant, the average energy of each particle
is
(A) 0
(B) 
(C)
4

3
(D) 2
(E) 3
解：由 Maxwell 分布，
E
0 e

1 e
当  << kT 时， e


kT

 3 e

kT
e

3
kT

kT
 1， E 

3
kT
。
4
。
3
答案选（C）
。
68. If a newly discovered particle X moves with a speed equal to the speed of light in vacuum,
then which of the following must be true?
(A) The rest mass of X is zero.
(B) The spin of X equals the spin of a photon.
(C) The charge of X is carried on its surface.
(D) X does not spin.
(E) X cannot be detected.
解：由相对论公式
E
m0
1
2
c2 。
v
c2
要使以光速运动的粒子的能量为有限值，则其静质量 m0 必须为零。答案选（A）
。
Question 69-71
A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic
Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on
both ends of the garage, which open automatically when the front of the car reaches them and
close automatically when the rear passes them. The opening or closing of each doorrequires a
negligible amount of time.
69. The velocity of the car in the garage’s rest frame is
(A) 0.4c
(B) 0.6c
(C) 0.8c
(D) greater than c
(E) not determinable from the data given
解：由大家熟知的公式， l  l 0 1 
v2
v2
l 3
，
1  2   ，解得 v=0.8c。答案选（C）。
2
c
l0 5
c
70. The length of the garage in the car’s rest frame is
(A) 2.4 m
(B) 4.0 m
(C) 5.0 m
(D) 8.3 m
(E) not determinable from the data given
解：利用上面的公式，且在车库参照系相对汽车参照系速度也为 0.8c，计算得 2.4m,答案选
（A）
。
71. Which of the following statements is the best response to the question:
“Was the car ever inside a closed garage?”
(A) No, because the car is longer than the garage in all reference frames.
(B) No, because the Lorentz contraction is not a “real” effect.
(C) Yes, because the car is shorter than the garage in all reference frames.
(D) Yes, because the answer to the question in the garage’s rest frame must apply in all reference
frames.
(E) There is no unique answer to the question, as the order of door openings and closings
depends on the reference frame.
解：一般人可能不敢选择（E）
，似乎一件事必须有个定论。其实不然，
“公说公有理，婆说
婆有理”也有可能。在车库参照系中，设后门坐标为 x = 0，且 t = 0 时刻后门开启，则后门
关闭的时空坐标为（0，
3
4
）,前门开启的时空坐标为（4，
）。两事件间的时空间隔
0 . 8c
0 . 8c
为 s  c t  x  0 ，为类空事件，即二者之间没有因果联系。所以不同参考系之间
2
2
2
2
说法不一并不矛盾。
72. The measured index of refraction of x-rays in rock salt is less than one. This is consisitent with
the theory of relativity because
(A) relativity deals with light waves traveling in a vacuum only
(B) x-rays cannot transmit signals
(C) x-ray photons have imaginary mass
(D) the theory of relativity predates the development of solid-state physics
(E) the phase velocity and group velocity are different
解：我们常用的公式 v 
c
中所指速度，为相速度 Vp。而相速度超光速是有可能的，因为
n
它不伴随着能量的传播。而群速度 Vg 才表示能量传播的速度，它不能超光速。在记一下两
个常用公式
Vp 

k
,
Vg 
d
。
dk
73. It is necessary to coat a glass lens with a nonreflecting layer. If the wavelength of the light in
the coating is , the best choice is a layer of material having an index of refraction between those
of glass and air and a thickness of

4

(B)
2
(A)
(C)

2
(D) 
(E) 1.5
解：为发生最大透射，从薄膜前后两表面反射的光波应干涉相消，即厚度 d 满 2d = (n+1/2)，
从而 d  (
n 1
 ) 。答案选（A）,对应 n = 0。此题未考虑半波损，这只当 1<n<nglass 时成立。
2 4
74. Unpolarized light is incident on two ideal polarizers in series. The polarizers are oriented so
that no light emerges through the second polarizer. A third polarizer is now inserted between the
first two and its orientation direction is continuously rotated through 180. The maximum fraction
of the incident power transmitted through all three polarizers is
(A) zero
1
8
1
(C)
2
(B)
(D)
1
2
(E) 1
解：光经过第一个偏振片后为线偏振光，强度为原来的 1/2（而不是 1/4，这地方容易出错），
则 I out 
I0
I
sin 2  cos 2  ，显然 = 450 时，Iout 最大，为 0 。答案选（B）。
2
8
75. The period of a hypothetical Earth satellite orbiting at sea level would be 80 minutes. In terms
of the Earth’s radius Re, the radius of a synchronous satellite orbit (period 27 hours) is most nearly
(A) 3 Re
(B) 7 Re
(C) 18 Re
(D) 320 Re
(E) 5800 Re
解：由向心力公式，m r 
2
GMm
2
27  60 81
4 2 3
2
,
其中


 ，
得，
T

r ，周期比
2
T
80
4
GM
r
由此得半径之比约为 7.4。答案选(B)。或者直接用开普勒第三定律，周期的平方与半径的立
方之比为常数，但是要切忌，这只是对绕同一天体运行的星体适用。
76. A hoop of mass M and radius R is at rest at the top of an inclined plane as shown above. The
hoop rolls down the plane without slipping. When the hoop reaches the bottom, its angular
momentum around its center of mass is
(A) MR gh
(B)
1
MR gh
2
(C) M 2 gh
(D) Mgh
(E)
1
Mgh
2
解：圆环的转动惯量为 I  MR 。由能量守恒，
2
1
1
Mv 2  I 2  Mgh （1），
2
2
由无滑滚动， R  v （2）
，
联立（1）式（2）式解得，  
gh
，所以角动量
R
L  I  MR 2 
gh
 MR gh 。
R
答案选（A）
。
77. A particle is constrained to move along the x-axis under the influence of the net force F=–kx
with amplitude A and frequency f, where k is a positive constant. When x=A/2, the particle’s
speed is
(A) 2fA
(B)
3fA
(C)
2fA
(D) fA
(E)
1
fA
3
1 2
kx 。由能量守恒，
2
1 2 1 A 2 1 2
kA  k ( )  mv
2
2 2
2
解：质点显然做简谐振动，势能为
解得
v
因为 f 
3k
3
A
A 。
4m
2
1 

，所以 v  3fA 。答案选(B)。
T 
78. A system consists of two charged particles of equal mass. Initially the particles are far apart,
have zero potential energy, and one particle has nonzero speed. If radiation is neglected, which of
the following is true of the total energy of the system?
(A) It is zero and remains zero.
(B) It is negative and constant.
(C) It is positive and constant.
(D) It is constant, but the sign cannot be determined unless the initial velocities of both particles
are known.
(E) It cannot be a constant of the motion because the particles exert force on each other.
解：开始时系统势能为 0，动能不为 0，从而动能为正值。故总能量为正。不考虑辐射，则
系统与外界无相互作用，能量守恒。答案选(C)。
79. One of Maxwell’s equations is   B  0 . Which of the following sketches shows magnetic
field lines that clearly violate this equation within the region bounded by the dashed lines?
解 ：（ A ） (B)(C)(E) 为 常 见 的 磁 力 线 。（ D ） 给 人 的 第 一 印 象 是 点 电 荷 的 电 力 线 ， 由


  E   /  0 ，梯度不为零。所以它代表磁力线时将导致   B  0 。答案选（B）。
80. Which of the following electric fields could exist in a finite region of space that contains no
charges? (in these expressions, A is a constant, and i, j, and k are unit vectors pointing in the x, y,
and z directions, respectively.)
(A) A(2xyi–xzk)
(B) A(–xyj+xzk)
(C) A(xzi+xzj)
(D) Axyz(i+j)
(E) Axyzi
解：由 Maxwell 方程组，

  E   /0 ，
本题中只有选项（B）
，




   xyj  xzk   x  x  0 ，空间处处无电荷。答案选（B）。
81. A small circular wire loop of radius a is located at the center of a much larger circular wire
loop of radius b sa shown above. The larger loop carries an alternating current I=I0cost, where I0
and  are constants. The magnetic field degenerated by the current in the large loop induces in the
small loop an emf that is approximately equal to which of the following? (Either use mks units
and let 0 be the permeability of free space, or use Gaussian units and let 0 be 4/c2.)
 0 I 0  a 2
  cos t
 2  b
(A) 
 0 I 0  a 2
(B) 
  sin t
 2  b
 0 I 0  a
 2  sin t
 2 b
(C) 
 0 I 0
 2
(D) 
 a
 2  cos t
b
 0 I 0  a
  sin t
 2 b
(E) 
解：由毕奥-萨伐尔定律
 
B 0
4

Idl  rˆ
 r2 ，
外环上各点在中心产生的磁感应方向相同，均垂直于圆环平面，易得
B
 0 2b
 I
I 0
2
4 b
2 b
因为 a << b,故内环磁感应强度近似为 B，则磁通量为
  a 2 B 
0 a 2
2
b
I
0 a 2
2
b
I 0 cos  t
所以感生电场
d  0 I 0  a 2


  sin t
dt
 2  b
答案选（B）
。
82. The emission spectrum of an atomic gas in a magnetic field differs from that of the gas in the
absence of a magnetic field. Which of the following is true of the phenomenon?
(A) It is called the Stern-Gerlach effect.
(B) It is called the Stark effect.
(C) It is due primarily to the nuclear magnetic moment of the atoms.
(D) The number of emission lines observed for the gas in a magnetic field is always twice the
number observed in the absence of a magnetic field.
(E) The number of emission lines observed for the gas in a magnetic field is either greater than or
equal to the number observed in the absence of a magnetic field.
解：为塞曼或反常塞曼效应，由于磁场的作用使能级简并解除，产生谱线分裂，。但正常塞
曼效应一般为三分裂，反常塞曼分裂可以是更多条。故答案(D)不对，选答案（E）
。选项(B)
Stark 效应也可产生谱线分裂，但是由电场造成的。
83. A spectral line is produced by a gas that is sufficiently dense that the mean time between
atomic collisions is much shorter than the mean lives of the atomic states responsible for the line.
Compared with the same line produced by a low-density gas, the line produced by the
higher-density gas will appear
(A) the same
(B) more highly polarized
(C) broader
(D) shifted toward the blue end of the spectrum
(E) split into a doublet
解：由能量时间测不准关系，
E   

，
2
能级的寿命越长，则其展宽越大。而在浓度较大的气体中，由于碰撞比较频繁，能级寿命短，
从而谱线宽度大。答案选（C）
。
84. Sodium has eleven electrons and the sequence in which energy levels fill in atoms is 1s, 2s, 2p,
3s, 3p, 4s, 3d, etc. What is the ground state of sodium in the usual notation 2S+1LJ?
(A)
1
S0
(B)
2
S1
2
(C)
1
P0
(D)
2
P1
2
(E)
3
P1
2
解：核外一共 11 个电子，其电子排布式为 1s 2 2s 2 2 p 6 3s 1 。总自旋角动量 S 和总轨道角动
量 L 由最外层 3s 电子决定。S = 1/2, L = 0, J = 1/2，所以基态为
2
S 1 ,答案选(B)。
2
85. The figure above shows the photon interaction cross section for lead in the energy range where
the Compton, photoelectric, and pair production processes all play a role. What is the correct
identification of these cross sections?
(A) 1=photoelectric, 2=Compton, 3=pair production
(B) 1=photoelectric, 2=pair production, 3=Compton
(C) 1=Compton, 2=pair production, 3=photoelectric
(D) 1=Compton, 2=photoelectric, 3=pair production
(E) 1=pair production, 2=photoelectric, 3=Compton
解：没读懂
86. The exponent in Coulomb’s inverse square law has been found to differ from two by less than
one part in a billion by measuring which of the following?
(A) The charge on an oil drop in the Millikan experiment
(B) the deflection of an electron beam in an electric field
(C) The neutrality of charge of an atom
(D) The electric force between two charged objects
(E) The electric field inside a charged conducting shell
解：如果库仑平方反比定律严格成立，则可以证明在均匀带电球壳内部电场处处为零。答案
选(E)。
87. In a gas of N diatomic molecules, two possible models for a classical description of a diatomic
molecule are:
Which of the following statements about this gas is true?
(A) Model I has a specific heat c v 
3
Nk .
2
(B) Model II has a smaller specific heat than Model I.
(C) Model I is always correct.
(D) Model II is always correct.
(E) The choice between Models I and II depends on the temperature.
解：在低温下，两个原子间距离这个振动自由度被冻结，此时可取模型 I。当温度较高时，
这个自由度被激发，须采用模型 II。答案选（E）
。答案(A)不对，模型 I 中两个原子共有 5
个自由度，由能均分定理， c v 
5
Nk 。
2
88. Consider a system of N noninteracting particles confined in a volume V at a temperature such
that the particles obey classical Boltzmann statistics. If the temperature is lowered to the point at
which quantum effects become important, the pressure of the gas may differ depending on
whether the particles are fermions or bosons. Let PF be the pressure if they are fermions, PB be the
pressure if they are bosons, and PC be the pressure the particles would exert if quantum effects are
ignored. Which of the following is true?
(A) PF = PB = PC
(B) PF > PC > PB
(C) PF > PB > PC
(D) PF < PB < PC
(E) PF < PC < PB
解：费米子有相互排斥的等效作用，压强变大；而玻色子有相互吸引的等效作用，压强变小。
答案选(B)。可以联想一下白矮星中子星中惊人的简并压，分别由电子和中子造成，均为费
米子。而玻色爱因斯坦凝聚则发生在玻色子之间。
89. A system containing two identical particles is described by a wave function of the form

1
2
 x  x    x  x 

1

2

1

2
where x1 and x2 represent the spatial coordinates of the particles and  and  represent all the
quantum numbers, including spin, of the states that they occupy. The particles might be
(A) electrons
(B) positrons
(C) protons
(D) neutrons
(E) deuterons
解：由交换对称性可知，应为玻色子。(A)、(B)、(C)、(D)分别为电子、正电子、质子、中
子，均为典型的费米子，交换反对称。(E)为氘核，为玻色子。答案选(E)。
90. The figure above shows one of the possible energy eigenfunctions (x) for a particle bouncing
freely back and forth along the x-axis between impenetrable walls located at x=–a and x=+a. The
potential energy equals zero for |x|<a. If the energy of the particle is 2 electron volts when it its in
the quantum state associated with this eigenfunction, what is its energy when it is in the quantum
state of lowest possible energy?
(A) 0 eV
(B)
1
eV
2
(C)
1
eV
2
(D) 1 eV
(E) 2 eV
解：只有一个节点，说明处于第一激发态，n = 2。由一维无限深势阱的能级公式
2k 2 2    2

  n ，
2m
2m  a 
2
En 
基态的能量 E0 
E1 1
 eV 。答案选（C）。
4 2
91. When a narrow beam of monoenergetic electrons impinges on the surface of a single metal
crystal at an angle of 30 degrees with the plane of the surface, first-order reflection is observed. If
the spacing of the reflecting crystal planes is known from x-ray measurements to be 3 angstroms,
the speed of the electrons is most nearly
(A) 1.410–4 m/s
(B) 2.4 m/s
(C) 5.0103 m/s
(D) 2.4106 m/s
(E) 4.5109 m/s
解：由 Bragg 公式
2d sin   n ，
本题中 n = 1， = 30 0。所以速度为
v
P
h
h


m m 2d sin 
带入数字计算，答案选(D)。
92. Which of the following is NOT compatible width the selection rule that controls electric dipole
emission of photons by excited states of atoms?
(A) n may have any negative integral value.
(B) l=1
(C) ml=0, 1
(D) s=1
(E) j=1
解：电偶极辐射的跃迁定则为：1.宇称改变；2. l=1；3. j=1, ml=0, 1。关键是光子由
角动量，但没有自旋，所以 s 的值无法改变。
93. An electric sander has a continuous belt that rubs against a wood surface as shown
schematically above. The sander is 100 percent efficient and draws a current of 9 amperes from a
120-volt line. The belt speed is 10 meter per second. If the sander is pushing against the wood
with a normal force of 100 newtons, the coefficient of friction is most nearly
(A) 0.02
(B) 0.2
(C) 0.4
(D) 1.1
(E) 10
解：功率全消耗在克服摩擦力上，所以 f 
P UI 120  9


 108 N ，摩擦系数为
v
v
10

f 108

 1.08  1.1 ，答案选(D)。
N 100
94. In the circuit shown above, R2=3R1 and the battery of emf (花体) has negligible internal
resistance. The resistance of the diode when it allows current to pass through it is also negligible
internal resistance. At time t=0, the switch S is closed and the currents and voltages are allowed to
reach their asymptotic values. Then at time t1, the switch is opened. Which of the following curves
most nearly represents the potential at point A as a function of time t?
解：技巧如下：在 t1 前瞬间，系统处于稳定状态，电感不起作用（
dI
 0 ），所以 A 点电
dt
压为 0，答案只能为(A)或（B）
；断开 S 前瞬间，
I

R1
。
故断开 S 后瞬间 A 点电压为
U A  IR2  3 。
答案选（B）
。
95. In the cycle shown above, KL and NM represent isotherms, while KN and LM represent
reversible adiabats. A system is carried through the Carnot cycle KLMN, taking in heat Q2 form
the hot reservoir T2 and releasing heat Q1 to the cold reservoir T1. All of the following statements
are true EXCEPT:
(A) Q1/T1=Q2/T2.
(B) The entropy of the hot reservoir decreases.
(C) The entropy of the system increases.
(D) The work W done is equal to the net heat absorbed, Q2–Q1.
(E) The efficiency of the cycle is independent of the working substance.
解：熵是态函数，所以经历一个循环后回到原来状态，熵值不变。答案选（C）。注意题目
中所指系统指循环系统，不包括热库等。大家可以用本题复习一下卡诺循环，其他几个选项
均是重要结论。
96. A particle of mass M is in an infinitely deep square well potential V where
V  0 for  a  x  a, and
V   for x  a, a  x.
A very small perturbing potential V’ is superimposed on V shuch that
a
a
a

V      x  for
 x  , and
2
2
2

a a
V   0 for x 
,  x..
2 2
If 0, 1, 2, 3, … are the energy eigenfunctions for a particle in the infinitely deep square well
potential, with 0 being the ground state, which of the following statements is correct about the
eigenfunction 0’ of a particle in the perturbed potential V+V’?
(A)
 0  a00 0 , a00  0

(B)  0 

(C)  0 

(D)  0 

a
n 0

a
n 0

a
n 0
 n with a0 n  0 for all odd values of n
0n
 n with a0 n  0 for all even values of n
0n
 n with a0 n  0 for all values of n
0n
(E) None of the above
解：V 和 V’均为偶宇称态，则
成正交完备组，所以
 0 必为偶宇称态。因为一维无限深势阱的全体本征态构
 0 可被它们展开。由于第 n 个本征态的宇称为（）n，所以不应有
n 为奇数的态的成分。答案选（B）
。
97. Two uniform cylindrical disks of identical mass M, radius R, and moment of inertia
1
MR 2 ,
2
as shown above, collide on a frictionless, horizontal surface. Disk I, having an initial
counterclockwise angular velocity 0 and a center-of-mass velocity v0 
1
 0 R to the right,
2
makes a grazing collision the two disks stick together, the magnitude of the total angular
momentum about the point P is
(A) zero
1
MR 2 0
2
1
MRv 0
(C)
2
(B)
(D) MRv0
(E) dependent on the time of the collision
解：碰撞前对于盘 I，质心角动量为
MV0 R 
1
M 0 R 2 ，
2
方向垂直纸面向里；而转动部分角动量为
I 0 
1
M 0 R 2 。
2
方向垂直纸面向外。两部分角动量大小相等方向相反，故总角动量为 0。因为碰撞前后相对
P 点的角动量守恒，所以碰撞后仍为 0。答案选（A）
。注意仔细看图，盘 I 不是做无滑滚动。
98. The long thin cylindrical glass rod shown above has length l and is insulated from its
surroundings. The rod has an excess charge Q uniformly distributed along its length. Assume the
electric potential to be zero at infinite distances from the electric potential at a point P along the
axis of the rod and a distance l from one end is
kQ
multiplied by
l
4
9
1
(B)
2
2
(C)
3
(A)
(D) ln 2
(E) 1
Q
dx
l
Q
l
 K ln 2 。答案选（D）。
解：电势 U   K
0
lx
l
99. The positronium “atom” consists of an electron and a positron bound together by their mutual
Coulomb attraction and moving about their center of mass, which is located halfway between
them. Thus the positronium “atom” is somewhat analogous to a hydrogen atom. The ground-state
binding energy of hydrogen is 13.6 electron volts. What is the ground-state binding energy of
positronium?
1
2
2
(A)    13.6 eV
(B)
1
 13.6 eV
2
(C) 13.6 eV
(D) 2  13.6 eV
(E) (2)2  13.6 eV
解：利用氢原子能级公式
En  
e 4 1
2 2 n 2
本题中电子偶素由于正负电子质量相同，折合质量  = me/2,而氢原子中  = me。所以电子
偶素基态能量为氢原子基态能级的一半。答案选(B)。请牢记氢原子（类氢原子）的能级公
式。
100. The screen of a pinhole camera is at a distance D from the pinhole, which has a diameter d.
The light has an effective wavelength . ( << D) For which of the following values of d will the
image be sharpest?
D
(A)
(B) 
(C)

10
(D)
(E)
2
D
D2

解：考试现场很可能不知道这个公式，不用慌，从量级上进行一下分析即可。~10-7m 量级，
D~10-2m 量级，而小孔的直径介于二者之间。选项中（B）(C)(D)答案太小，10-7m 量级的小
孔怎么能用来照相。选项(E)答案太大。答案选(A)。