58. The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax. ψ(x) = 0 for x ＜ 0 and x ＞ L. When the wave function is normalized, the probability density at coordinate x has the value ______.
(A) 2x/L²
(B) 2x² /L²
(C) 2x² /L³
(D) 3x² /L³
(E) 2x³ /L³

54. A beam of unpolarized light of intensity I0 passes through four successive ideal polarizing filters, each of whose polarizing axis makes a 30° angle with the previous one. What is the intensity of the transmitted beam? (A) 1 (B) 81/256 (C) 27/128 (D) 9/16 (E) 0

55. When sitting in an airplane at an altitude of 10 km, you look down on the ground. Assuming that your pupil is about 1.5 mm in radius and considering the effect of diffraction only, what is the minimum separation s between objects on the ground that you can distinguish? (The wavelength of visible light is around 500 nm.) (A) 0.5 m (B) 2 m (C) 8 m (D) 20 m (E) 50 m

56. A spaceship S1 is moving away from us at a speed of 0.8 c. Another spaceship S2 is moving away from us in the opposite direction at a speed of 0.5 c. What is the speed of S1 measured by an observer on S2? (A) 1.3 c (B) 1.0 c (C) 0.97 c (D) 0.93 c (E) 0.89 c

57. Silicon (Si) is a semiconductor material whose properties fit perfectly in solar cells to convert the light energy into electrical energy. Based on this evidence, what the value of energy gap of Si probably is? (A) several tenths of eV (B) 1.1 eV (C) 3.1 eV (D) 5.1 eV (E) 7.1 eV

59. A light of wavelength 400 nm falls on a metal surface having a work function 1.70 eV. What is the maximum kinetic energy of the photoelectrons emitted from the metal?( c = 3.00 × 108 m/s, h = 6.626 × 10-34 J●s , 1 eV = 1.60 × 10-19 J) (A) 4.52 eV (B) 3.11 eV (C) 2.82 eV (D) 1.70 eV (E) 1.41 eV

60. The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 2 as shown in the figure. Consider the photon of the longest wavelength corresponding to a transition shown. What is its wavelength?(A) 420 nm (B) 458 nm (C) 540 nm (D) 656 nm (E) 720 nm

61. Which structure is not considered to have aromaticity? (A)(B)(C)(D)(E)

62. Solid KF has a lattice energy of –804 kJ/mol and a heat of solution (in water) of –15 kJ/mol. RbF has a lattice energy of –768 kJ/mol and a heat of solution (in water) of –24 kJ/mol. Which salt forms stronger attractions with water? (A) KF, because it releases more heat during the formation of crystal. (B) KF, because it has a more negative heat of hydration. (C) RbF, because it releases more heat during the formation of crystal. (D) RbF, because it has a more negative heat of hydration. (E) Both salts have the same interactions with water.

【已刪除】63. The reaction 2NO2 → 2NO + O2 obeys the rate law at 400 K. If the initial concentration of NO2 is 1.00 M, how long will it take for the [NO2] to decrease to 0.25 M ? (A) 50 s (B) 100 s (C) 200 s (D) 300 s (E) 600 s

64. Today’s automatic sunglasses utilize the following rearrangement reaction between A and B promoted by UV:However, infrared spectroscopy is often applied to differentiate A and B because of the strong and distinct absorption of _________ functional group.(A) arene (B) conjugated olefin (C) carbonyl (D) ether (E) amide