複選題

13. Which of the following statements are correct?
(A) The Maxwell-Boltzmann distribution function holds for identical particles that are sufficiently far apart to be distinguishable.
(B) Bosons are particles whose spin are 0 or an integer and have wavefunctions that are asymmetric to an exchange of any pair of them.
(C) The bosons do not obey the exclusion principle and the Bose-Einstein distribution function may be exploited for them.
(D) Electrons are fermions and we shall use Fermi-Dirac statistics to study the behavior of the free electrons in a metal that are responsible for its ability to conduct electric current.
(E) None of the above.

14. Electrons are accelerated through an electric potential V and then fall on a pair of slits that have a separation of 100 nm. The resultant interference pattern indicates that the electrons have a wavelength of 1.0 nm. Which of the following statements are correct? (A) The momentum of one of the electrons is about 6.63×10⁻²⁵ kg·m/s. (B) The accelerating electric potential V is about 1.50 Volts. (C) The minimum spread in the momentum of electron in the direction parallel to the plane of the slits is about 5.27×10⁻²⁸ kg·m/s. (D) The velocity of electron is about 7.25×10⁴ m/s. (E) All statements are correct.

15. For a neutron with given kinetic energy KE = 23.5 MeV to calculate the momentum p, de-Broglie wave length λd, velocity v, and uncertainty of the position Δx, and an electron with the same Δx to calculate the KE, p, λd, and v of the electron. (A) Neutron: p = 125.5 MeV/c, λd = 1.482×10⁻¹⁴ m, v = 4.565×10⁷ m/s, Δx = 5.366×10⁻¹⁵ m (B) Neutron: p = 105.5 MeV/c, λd = 1.186×10⁻¹⁴ m, v = 3.355×10⁷ m/s, Δx = 4.635×10⁻¹⁶ m (C) Neutron: p = 211.5 MeV/c, λd = 5.863×10⁻¹⁵ m, v = 6.581×10⁷ m/s, Δx = 9.217×10⁻¹⁶ m (D) Electron: KE = 26.64 MeV, p = 53.5 MeV/c, λd = 2.316×10⁻¹⁴ m, v = 1.498×10⁸ m/s (E) Electron: KE = 106.55 MeV, p = 107.06 MeV/c, λd = 1.158×10⁻¹⁴ m

16. For lattice vibration in a crystal with the atomic mass of m, provide the potential energy U(x) in one dimension x to solve the wave function Ψ(x), the oscillation frequency ω, the quantum energy En, zero-point energy ε₀, and average energy ⟨E⟩ at temperature T under the condition of the probability function P(En) = e-En/keT to calculate ⟨E⟩ at T ≅ 0 and ⟨E⟩ at very high temperature. (A) Ψ(x) = (2ⁿn!)^ Hn(x) e-(mωx)²/2ℏ), ω =, H₀(x) = 1, H₁(x) = 2x (B)(C) (D) U(x) =kx², ⟨E⟩ ≅ ℏω/2 at T ≅ 0, ⟨E⟩ ≅ kBT at very high T (E)

17. The wavelength of a beam of light is increased but the light's intensity remains unchanged. Which of the followings are true? (A) There are fewer photons per second. (B) There are more photons per second. (C) Each photon has less energy. (D) Each photon has more energy. (E) Nothing happens to the photon number because the light is a wave.

複選題18. Consider a p-n diode. Which of the following are correct? (A) Near the p-n junction, electrons and holes diffuse and recombine, resulting in a depletion region. (B) When forward biased, there will be electrons flowing from n side to p side. (C) When forward biased, there will be holes flowing from p side to n side. (D) When unbiased, the Fermi energy is aligned throughout the diode. (E) When unbiased, the conduction band edge is aligned throughout the diode.

19. Consider the angular momentum of an electron in the 2Pz orbital of hydrogen atom. Which of the following are wrong? (A) The electron has a nonvanishing projection of angular momentum in the z direction. (B) If the projection of electron angular momentum in the x direction is measured, it always yields zero. (C) If the total electron angular momentum is measured, it yields a distribution with a finite width. (D) If the projection of electron angular momentum in the z direction is measured, it always yields an identical value. (E) If a magnetic field in the z direction is applied, it will shift the electron energy.

20. For the following normalized real wavefunctions, ΨA(x), ΨB(x) and ΨC(x), versus x for a particle in which of the following statements are correct? (A) The wavefunction ΨB(x) will yield the largest value for ⟨x⟩. (B) The wavefunction ΨC(x) will yield the largest value for ⟨x²⟩. (C) The wavefunction ΨC(x) will correspond to the highest kinetic energy. (D) All wavefunctions ΨA(x), ΨB(x) and ΨC(x) will yield the largest value for ⟨x⟩. (E) All wavefunctions ΨA(x), ΨB(x) and ΨC(x) will yield the largest value for ⟨x²⟩.

51.依民法規定，出租人就租賃物所受損害對於承租人之賠償請求權時效，從何時起算？(A)自租賃關係終止時起算(B)自受損害時起算(C)自受租賃物返還時起算(D)自受受損害時起算30日起算

52.依民法規定，承租人之償還費用請求權及工作物取回權之請求權時效，從何時起算？(A)自租賃關係終止時起算(B)自請求之日起算(C)自租賃物返還時起算(D)自請求日後30日起算

53.依民法規定，下列何者非屬承租人可以終止租賃契約?(A)危及安全或健康之瑕疵(B)出租人逾期不修繕(C)第三人主張權利，但不影響承租人使用(D)房屋部分滅失，存餘部分不能達租賃之目的

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