複選題

11. Consider the following optical phenomena, which ones of them can be deduced from Fermat's principle of least time?
(A) single slit diffraction
(B) double slit interference
(C) reflection law (The angle of incidence is equal to the angle of reflection.)
(D) refraction law (Snell's law)
(E) zero reflection at Brewster's angle

12. Continued from the last question, which ones of them can be deduced from Maxwell's theory of electromagnetism?(A) single slit diffraction(B) double slit interference(C) reflection law (The angle of incidence is equal to the angle of reflection.)(D) refraction law (Snell's law)(E) zero reflection at Brewster's angle

複選題13. Which ones of the following statements are the postulates of special relativity?(A) No object can moves with a speed higher than the speed of light in vacuum.(B) The speed of light in vacuum is the same in all inertial reference frames.(C) E = mc², where E is energy, m is mass, and c is speed of light in vacuum.(D) The space-time transformation obeys the Lorentz transformation.(E) All physical laws have the same form in all inertial reference frames.

14. In quantum mechanics, every dynamic variable is represented as an operator. Consider the position representation, which ones of the following statements are correct?(A) the momentum operator along x-axis is px = m (∂x/∂t)(B) the momentum operator along x-axis is px = −im (∂x/∂t)(C) the momentum operator along x-axis is px = −iℏ (∂/∂x)(D) the angular momentum operator is L = −iℏ (r × ∇)(E) the angular momentum operator is L = iℏ (∇× r)

複選題15. Which ones of the following requirements are sufficient conditions for a ferromagnetic material?(A) The atoms of the material must have permanent magnetic dipole moment.(B) The atoms of the material must have no permanent magnetic dipole moment.(C) The atoms may or may not have permanent magnetic dipole moment.(D) There is no interaction between the atomic dipoles.(E) There are strong interactions between the atomic dipoles.

16. According to Planck's theory, which ones of the following quantities must be quantized to explain the spectrum of blackbody radiation?(A) spin of electrons(B) energy of electrons(C) momentum of electromagnetic waves(D) energy of electromagnetic waves(E) energy transfer between electromagnetic waves and electric oscillators

17. Consider the electromagnetic Poynting vector (S = E × H), which ones of the following statements are correct?(A) Poynting vector is the energy flux density of electromagnetic field.(B) Poynting vector is the momentum flux density of electromagnetic field.(C) Poynting vector is proportional to the momentum density of electromagnetic field.(D) Poynting vector is proportional to the angular momentum density of electromagnetic field.(E) Poynting vector is proportional to the optical pressure of an electromagnetic wave.

複選題18. Consider the entropy of an ideal gas system, which ones of the following processes result in the increase of its entropy?(A) Quasi-static isothermal expansion from volume V to volume 2V.(B) Quasi-static isothermal compression from e V to volume (1/2)V.(C) Adiabatic free expansion from volume V to volume 2V.(D) Quasi-static adiabatic expansion from volume V to volume 2V.(E) Quasi-static adiabatic compression from volume V to volume (1/2)V.

19. Consider a typical LRC circuit shown in the figure. The capacitor ( C ) is initially charged and the switch (S) is closed at time t = 0. Then the current oscillates in the circuit. Which ones of the following statement are correct? (A) If the inductance is increased, the oscillation frequency will be increased.(B) If the inductance is increased, the oscillation frequency will be decreased.(C) If the resistance is increased, the damping of the oscillation is increased.(D) If the resistance is increased, the damping of the oscillation is decreased.(E) If the inductance is increased, the damping of the oscillation is decreased.

20. Consider the Schrödinger equation, which ones of the following descriptions of the wave function Ψ(x, t) are correct?(A) The probability of finding the particle at position x and time t is proportional to |Ψ(x, t)|².(B) The mass distribution of a particle at position x and time t is proportional to |Ψ(x, t)|².(C) The mass distribution of a particle at position x and time t is proportional to |Ψ(x, t)|.(D) If Ψ₁ and Ψ₂ are two possible wave functions to describe the state of a particle. Then Ψ₃ = (2/5) Ψ₁ + (3/5) Ψ₂ may be another state of the particle(E) If Ψ₁ and Ψ₂ are two possible wave functions to describe the state of a particle. Then Ψ₃ = (3/5) Ψ₁ + (4/5) Ψ₂ may be another state of the particle

1. 如右圖之玻璃管，口徑為 0.50 公分，於 25℃，1 大氣壓時，已知左方玻璃管上方密閉空間中的氣體為氦氣，其體積為 5 毫升，此時左右玻璃管中之汞柱高度差為 14 公分。假設氦氣可視同理想氣體，今在右方開口處加入一些汞，使得最終左右汞柱高度差為 24 公分，試問此時氦氣的體積為若干毫升？ (A)2.5 (B)3.5 (C)4.0 (D)4.5 (E)4.9

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