所屬科目：研究所、轉學考(插大)-近代物理學
1．An alien spaceship streaks past the football stadium along the direction of play at 0.6c (as measured by the players on the field). A football field is 120 yards long by 55 yards wide. What is the length of the football field according to the alien? (A)120 yards (B)150 yards (C)96 yards (D)189.7 yards (E)75.9 yards
2．A spaceship whose rest length is 300.0 m has a speed of 0.80c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.80c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the spaceship? (A)1.110 μs (B)1.080 μs (C)1.055 μs (D)1.025 μs (E)1.010 μs
3．Two identical objects, each of rest mass m₀, moving with equal but opposite velocities of 0.60c in the laboratory reference frame, collide and stick together. The resulting particle has a rest mass M₀. Is M₀ equal to (A)1.5 m₀ (B)2.0 m₀ (C)2.5 m₀ (D)3.0 m₀ (E)3.5 m₀
4．Which of the following phenomena most clearly demonstrates the wave nature of electrons? (A)The photoelectric effect. (B)Blackbody radiation (C)The Compton effect. (D)Diffraction of electrons by crystals. (E)None of these answers.
5．A thermal neutron has a speed v at temperature T=300 K and kinetic energy mₙv²/2=3kT/2. By Heisenberg's Uncertainty principle, what is the estimated kinetic energy (in MeV) of a nucleon bound within a nucleus of radius 10⁻¹⁵ m? (A)960.48 (B)763 (C)20.48 (D)197.48 (E)177
6．A hydrogen atom is in an excited state with the electron in a p-shell. Which of the following sets of quantum numbers n, ℓ, m is not consistent with this statement? (A)n, ℓ, m = 1, 1, 0. (B)n, ℓ, m = 2, 1, 1. (C)n, ℓ, m = 2, 1, 0. (D)n, ℓ, m = 2, 1, -1. (E)n, ℓ, m = 3, 1, 0.
7．Consider the electrons in a 1D metal and describe them as free particles. Let E(k)=p²/2m be the energy of an electron with momentum p. Then, the corresponding phase velocity of the electron wave is given by (A)p/m (B)p/(2m) (C)2p/m (D)21/2 p/m (E)None of the above
8．Consider two free electrons in 1D having the same wave vector k but opposite spins . Which of the following expressions gives the correct, normalized wave function for the two electrons? (A) (B) (C) (D) (E)None of the above
9．Which are the following statements correct?
(A)The maximum kinetic energy of the recoil electron in Compton scattering is given by ,where f is the frequency of the incident photon, h the Plank constant, c speed of the light and m rest mass of an electron.
(B)The black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature.
(C)The photon is massless so that the gravitational force will not affect its frequency as it leaves a star.
(D)The maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident light.
(E)x-rays were found to be unaffected by electric and magnetic fields, to pass readily through opaque materials and to cause phosphorescent to glow.
10．X-rays having energy of 250 keV undergo Compton scattering from a target. The scattered rays are detected at 41° relative to the incident rays. (sin41°=0.656, cos41°=0.7547) Which of the following statements are true: (A)The wavelength of incident X-ray is 4.96×10⁻³ nm. (B)The Compton wavelength shift at this angle is 5.15×10⁻⁴ nm. (C)The wavelength of scattered X-ray is 5.95×10⁻³ nm. (D)The energy of the scattered X-ray is 223.2 keV. (E)The kinetic energy of the recoiling electron is 26.8 keV.
11．Which are the following statements correct? (A)At every instant the ratio of the magnitude of the electric field to the magnitude of the magnetic field in an EM wave equals the speed of light. (B)The instant energy density associated with the magnetic field of an EM wave equals to the instant density associated with the electric field. (C)The intensity of an EM wave is proportional to the cube of the amplitude of magnetic field. (D)Classical wave equation is invariant under Galileo transformation. (E)The intensity of an EM wave equals the average energy density multiplied by the speed of light.
12．Ytterbium (Yb) has a work function φ=2.6 eV. Which of the following statements are true: (A)The lowest frequency f that can liberate an electron from Yb is 6.29×10¹³ Hz. (B)The longest wavelength λ that can liberate an electron from Yb is 476.9 nm. (C)Suppose light with wavelength λ=257 nm impacts some Yb. The voltage Vmax that the liberated electrons from Yb can overcome is 2.23 V. (D)When an unknown light is shone on Yb, it is found that the electrons can only overcome a voltage of Vmax=1.75 V. The wavelength of light is 708.6 nm. (E)None of the above
13．Which of the following are true for photons? (A)Photons are Bose particles. (B)Two photons are not allowed to occupy the same quantum state. (C)They obey Bose-Einstein distribution with a finite chemical potential. (D)Inside a cavity, the average photon number in a specific cavity mode (with frequency f) is approximately given by kBT/(hf), h=Planck constant, when kBT/h＞＞f. (E)None of the above.
14．Which of the following are true for electrons? (A)The same quantum state cannot be occupied by more than one electron. (B)Two electrons can have the same spin state. (C)At any temperature, electrons in a solid cannot be found above the Fermi level EF. (D)The existence of energy gap in a semiconductor can be proved within quantum physics. (E)None of the above.
15．Consider the Schrödinger Equation for the time-dependent state vector ψ(x,t) of a system︰=Hψ (x,t).Assume we can find a funcition ψE(x) such that it is an eigenstate to the Hamiltonian H: HEψ(x) = EψE(x). Which of the following statements are true? (A)A complete solution is given by ψ(x,t)=φE(x). (B)A complete solution is given by ψ(x,t)=φE(x)exp. (C)The full solution can be written as a product c(t)φE(x), where c(t) is some complex function of time. (D)The function c(t) above can have any arbitrary functional form. (E)If measured at some future time, the energy of the system described by c(t)φE(x) is E.
16．Which of the following statements are correct? (A)If electrons have been accelerated from rest through a potential difference of 54 V, then the wavelength of electrons is 1.667 nm. (B)For high principle quantum number (n) for hydrogen atom, the spacing between the neighboring energy levels is proportional to 1/n³. (C)A particle of mass mₑ trapped in an infinite depth well of width L=1 nm. The transition from excited state n=2 to ground state n=1. The wavelength of light emitted is 886.4 nm. (D)The relation for total energy E and momentum p for a relativistic particle is E²=c²p²+m²c⁴. The product of group velocity and the phase velocity is equal to c². (E)If the electron wave function is Ce^(ikx) between x=2 and x=22 cm, zero everywhere else. The probability of finding the electron between x=0 and x=4 cm is 0.1.
(A) Plot the all three potential energy U per ion pair versus separation distance r, and indicate the equilibrium distance r0 and equilibrium potential energy U0.
(B) Determinate the equilibrium (minimum) potential energy U0.
(A) the operation principle of LED.
(B) Illustrate (畫圖說明) the operation principle of solar cell (SC).
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(B)
(C)
(D)
(E)None of the above
,where f is the frequency of the incident photon, h the Plank constant, c speed of the light and m rest mass of an electron.
=Hψ (x,t).Assume we can find a funcition ψE(x) such that it is an eigenstate to the Hamiltonian H: HEψ(x) = EψE(x). Which of the following statements are true? (A)A complete solution is given by ψ(x,t)=φE(x). (B)A complete solution is given by ψ(x,t)=φE(x)exp
. (C)The full solution can be written as a product c(t)φE(x), where c(t) is some complex function of time. (D)The function c(t) above can have any arbitrary functional form. (E)If measured at some future time, the energy of the system described by c(t)φE(x) is E.