53. A light beam of wavelength λ is travelling along a direction making an angle of 60° with a positive x-axis and 30° with a positive y-axis. Find the phase difference between two points (√3,1,2) and (0,0,0).
(A) √3π/λ
(B) 2√3π/λ
(C) 3√3π/λ
(D) 4√3π/λ
(E) 5√3π/λ

54. In the context of the Bohr model of the hydrogen atom, what happens when an electron transitions from a higher energy level to a lower energy level? (A) A photon is emitted. (B) The mass of the atom decreases significantly. (C) The electron stops moving. (D) A photon is absorbed. (E) All of the above.

55. An electron is trapped in an one-dimensional box of finite width whose walls are perfectly rigid (infinite deep square well potential). A photon with energy Ea is emitted when the electron transitions from the n = 4 to n = 2, and a photon with energy Eb is emitted when the electron transitions from the n = 3 to n = 1. What is the ratio of Ea / Eb? (A) 2/3 (B) 3/2 (C) 1 (D) 4/3 (E) It depends on the width of the potential well.

56. A patient is injected with a radioactive tracer that has a physical half-life of 6 hours. If the initial activity of the tracer in the patient's body is 400 MBq, what will the activity be after 24 hours? (Assume no biological clearance occurs during this time). [unit: becquerel (Bq)=1decay/second] (A) 400 MBq (B) 200 MBq (C) 100 MBq (D) 50 MBq (E) 25 MBq

57. A drug has a half-life of 4 hours. The minimum effective concentration is 25 mg and the toxic threshold is 150 mg. If each tablet contains 100 mg, what is the dosing window to ensure the patient stays within the therapeutic range? (A) every 2 to 4 hours (B) every 4 to 8 hours (C) every 8 to 12 hours (D) every 12 to 16 hours (E) every 16 to 24 hours

58. Consider hydrogen-like atoms (atomic number = Z) that are at excited state with some principal quantum number n. It is found that the emission spectrum has 6 different lines. Furthermore, the most energetic photon in the emission spectrum has an energy of 51 eV. Find the atomic number Z. [Hydrogen atom En = -13.6/n2 (eV)] (A) 5 (B) 4 (C) 3 (D) 2 (E) 1

59. According to the Beer-Lambert Law, how many half-value layers are required to reduce the intensity of X-rays to 1/80 of their original intensity? [log10 2 = 0.301] (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

60. Positron Emission Tomography is a highly advanced imaging technology in modern medicine. PET is primarily used to observe cellular metabolism; this is especially useful for cancer. After the isotope in the radiopharmaceutical enters the body, it migrates to the lesion site and emits a positron. As the positron moves through the tissue, it strikes an electron within the body. When the two collide, annihilation occurs, converting matter into energy and emitting two gamma rays of equal energy. The detectors then use these two rays to calculate the precise location of the lesion. Assume that both the electron and the positron carry a kinetic energy K=0.23m0c2, where m0 is the rest mass of an electron and c is the speed of light. What is the wavelength of the gamma rays produced after a head-on collision? [Compton wavelength is λ0=h/(m0c), where h is Planck's constant] (A) λ = 2.83 λ0 (B) λ = 1.62 λ0 (C) λ = 0.81 λ0 (D) λ = 0.40 λ0 (E) λ = 0.25 λ0

61. If (S)-1-bromo-2-methylbutane undergoes radical bromination at the chiral center, is the obtained major product (or mixture of products) optically active? (A) Yes, (S) (B) Yes, (R) (C) No, racemic (D) No, due to symmetry (E) Depends on temperature

62. How many of the following electron configurations for the species in their ground state are correct? Ca: 1s2 2s2 2p6 3s2 3p6 4s1     Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p4     V: [Ar] 3s2 3d3 As: [Ar] 4s2 3d10 4p2  P: 1s2 2s2 2p6 3p5 (A) 1 (B) 2 (C) 3 (D) 4 (E) None of the above

63. Which of the following techniques is best for determining the molecular weight? (A) IR (B) UV-Vis (C) Mass Spectrometry (D) NMR (E) CD

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