7. Suppose you are in a spaceship travelling through the solar system at a constant speed of v = 1.5×10⁸ m/s relative to Mars. You fire a pulse of laser light out the back of your vessel (i.e. in the direction from where you came from). How fast does an inertial observer on Mars see the pulse leave your ship?
(A) 1.5×10⁸ m/s
(B) 2.4×10⁸ m/s
(C) 3×10⁸ m/s
(D) 4.5×10⁸ m/s
(E) Something else.

8. Bohr model was derived as a primitive model of Hydrogen atom, which can calculate the orbital radius, wavelength, speed, period, and energies of the electron. Please make required modification on the original Bohr model to calculate r₁, λ₁, v₁, E₁, E₂, and v_α for a muon with m_u = 220 m_e captured by a proton to form a muonic atom. v_α is the photon frequency for transition from E₂ to E₁ (α-line). (A) r₁ = 1.256×10⁻¹³ m, λ₁ = 7.892×10⁻¹³ m, v₁ = 2.35×10⁶ m/s, E₁ = −3668 eV, E₂ = −917 eV, vα = 6.651×10¹⁷ Hz (B) r₁ = 1.865×10⁻¹³ m, λ₁ = 1.172×10⁻¹² m, v₁ = 2.35×10⁶ m/s, E₁ = −3164 eV, E₂ = −791 eV, vα = 5.737×10¹⁷ Hz (C) r₁ = 2.185×10⁻¹³ m, λ₁ = 1.373×10⁻¹² m, v₁ = 2.22×10⁶ m/s, E₁ = −2816 eV, E₂ = −704 eV, vα = 5.106×10¹⁷ Hz (D) r₁ = 2.694×10⁻¹³ m, λ₁ = 1.693×10⁻¹² m, v₁ = 2.187×10⁶ m/s, E₁ = −2672 eV, E₂ = −668 eV, vα = 4.845×10¹⁷ Hz (E) r₁ = 3.068×10⁻¹³ m, λ₁ = 1.928×10⁻¹² m, v₁ = 2.198×10⁶ m/s, E₁ = −2316 eV, E₂ = −579 eV, vα = 4.2×10¹⁷ Hz

9. For an electron with a de-Broglie wavelength of 2.425×10⁻¹² m, please find the correct the momentum p, kinetic energy KE, rest energy E₀, total energy E, and velocity v of the electron and phase velocity vp. (A) p = 2.7324×10⁻²² kg·m/s, v = 2.9995×10⁸ m/s, KE = 4.0978×10⁻¹⁴ Joule (B) E₀ = 8.1876×10⁻¹⁴ Joule, KE = 4.0978×10⁻¹⁴ Joule, E = 1.2285×10⁻¹³ Joule (C) p = 511 KeV/c, KE = 212 KeV, v = 2.12×10⁸ m/s, vp = 4.2388×10⁸ m/s ＞ c (D) p = 511 KeV/c, KE = 212 KeV, E = 723 KeV, v = 2.73×10⁸ m/s, vp = 3.2925×10⁸ m/s ＞ c (E) p = 511 KeV/c, KE = 255.8 KeV, v = 2.9995×10⁸ m/s, vp = 2.9965×10⁸ m/s

10. You do the photoelectric effect with a big chunk of Gold (work function= 5.1 eV), which you happened to have to lying around in your room. You find that with the light source you have at hand, you get a stopping potential of 1.1 V. What is the wavelength of your light source? (A) 150 nm (B) 200 nm (C) 300 nm (D) None of the above. (E) Cannot tell, because there is not enough information to calculate this.

11. The Michelson-Morley experiment tests if the speed of light in all inertial frames... (Please choose the following statements that are incorrect.) (A) ...is the same in air and in vacuum. (B) ...is the same in accelerating frame. (C) ...is the same in all directions. (D) ...depends on the wavelength or color. (E) ...changes when reflected by mirror.

12. The measured conductivity of copper at room temperature is 5.88×10⁷ Ω⁻¹m⁻¹ and the Fermi energy of copper is 7.03 eV. Assume that each copper atom contributes one electron to the electron gas. The density and molar mass of copper are 8.96 g/cm³ and 63.5 g/mole, respectively. Which of the followings are correct? (A) The electron density in copper is about 8.5×10²⁸ electrons/m³. (B) The average time between collisions is about 2.46×10⁻¹⁴ s. (C) The Fermi velocity is about 1.57×10⁷ m/s. (D) The mean free path is about 3.86×10⁻⁷ m. (E) All statements are correct.

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.

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