課程名稱︰普通物理甲下
課程性質︰
課程教師︰郭光宇
開課系所︰化學系
考試時間︰2005.06.21 10:25~12:15
試題：
1. (24%)simple questions and answers i P i
(1)figure one shows a parallel-plate capacitor and the current ←│‧│←
in the connecting wires that is discharging the capacitor. ─┤ ├─
Are the directions of(a)electrical field E and │ │
(b)displacement current i(d) leftward or rightward between ↑fig.1
the plates? (c)is the magnetic field at point P into or
out of the page?
air
(2)figure 2 shows four long horizontal layers of different ──────
materials,with air above and below them.The index of ↗ 1.3
refraction of each material is given. Rays of light are ──────
sent into the left ends of each material is given. In ↗ 1.5
which layer 1is there the possibility of totally trapping ──────
the light in that layer so that after many reflection, ↗ 1.4
all the light reaches the right end of the layer? ──────
↗ 1.3
→fig.2 ──────
air
(3)You are conducting a single-slit diffraction experiment
with light of wavelength λ.What appears, on a distant viewing screen,
at a point which the top and bottom rays through the slit have a path
difference equal to (a)5λ and (b) 4.5λ?
(4)According to the theory of relativity, which of the following statements
is true? (a)moving clocks runs fast. (b) energy is not conserved in high
speed collitions. (c) the speed of light must be measured relative to
the ether. (d)momentum is not conserved in high speed collisions.
(e) non of the (a),(b),(c)and(d)are true.
(5)Three electrons are trapped in three different 1-D infinite potential
wells of widths(a)0.5Α (b)2.0Α,and(c)1.0Α. Rank the electrons according
to their ground-state energies, greatest first.
(6)Consider the element chlorine (Z=17). In its part of the periodic table,
the subshells of the electronic states are filled in the sequence
1s 2s 2p 3s 3p 3d 4s 4p... Identify the highest occupied subshell and
state how many electrons are in it.
2.(9%)You want to rotate the plane of polarization of a polarized light beam
by 45 degrees with a Max intensity reduction of 10% (a) How many sheets
of perfect polarizers do you need to achieve your goal? (b) What is the
angle between adjacent polarizers?
3.(9%)It has been proposed that a spaceship might be propelled in the solar
system by radiation pressure, using a large sail made of foil. How large
must the sail be if the radiation force is to be equal in magnitude in
the sail be if the radiation force is to be equal in magnitude in the
Sun's gravitational attraction? Assume that the mass of the ship+sail is
1500kg, that the sail is perfectly reflecting, and that the sail is
oriented perpendicular to the sun's rays. The mass and the radiation
power of the sun are 1.99*10^30 kg and 3.9*10^26 W, respectively. The
gravitational constant G is 6.67*10^-11 (With larger sail, the ship is
continually driven away from the sun.)
↓↓↓↓↓↓
4.(10%) Figure 3 shows a transparent plastic block ────────┐
with a thin wedge of air at right.(The wedge │
thickness is exaggerated in the figure.) A broad ˍ▂▃▅█
beam of red light, with wavelength λ=632.8nm, ▇▅▃ˍ
is directed downward through the top of the block │
(at an incidence angle of 0 degree). Some of the ────────┘
light is reflected back up from the top of the
wedge, which act as a thin film(of air) with a
thickness that varies uniformly and gradually from
Ll at the left-hand end to Lr at the right-hand end.(The plastic layers
above and below the wedge of air are too thick to act as thin films.)
An observer looking down the block sees an interference pattern consisting
of six dark fringes and five bright red fringes along the wedge. What is
the change in thickness △L=Lr-Ll along the wedge?
5.(10%) The first-order diffraction maximum is observed at 12.6degrees for a
crystal in which the interplanar spacing is 0.24 nm. How many other
orders can be observed?
6.(9%) A meter stick in frame S' makes an angle of 30 degrees with the x' axis.
If that frame moves parrallel to the x axis of frame S with speed of 0.90c
relative to frame S, what is the length of the stick as measured from S?
7.(9%)In a photoelectric experiment using a sodium surface, you find a stopping
potential of 1.85V for a wavelength of 300nm and a stopping potential of
0.82V for a wavelength of 400nm. From these data find (a) a value for
Prank's Constant, (b) the work function ψfor sodium, and(c) the cut off
wavelength λo for sodium.
8.(10%)The ground state wave function of the hydrogen atom is Ψ(r)=e^(-r/a)
/√π^(a^2/3) where a=0.529Α is the Bohr radius. (a) What is the radial
probability density P(r)? (b)Find the radius r at which the radial
probability density has the maximum value.
9.(10%) Seven electrons are confined to a sqaure corral that is a 2-D infinite
potential well with widths Lx=Ly=L. Assume that the electrons do not
electrically interact with one another. (a) What is the electron
configuration for the ground state of the system of seven electrons?
(b)What is the total energy of the seven-electron system in its ground
state, as a multiple of h^2/8mL^2 ?
(c)How much energy must be transfered to the system for its jump to its
first excited satae, and what is the energy of that state?
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