50. A circular loop having a diameter of 10 cm carries a current of 0.1 ampere. The loop is placed in a magnetic field of B = 0.5 tesla with its axis inclined at 30° to the direction of the B-field as shown in the figure. Calculate the torque exerted on the current loop. [unit: newton (N)]

(A) 1.96×10^-4 N·m
(B) 3.97×10^-4 N·m
(C) 5.43×10^-4 N·m
(D) 7.22×10^-4 N·m
(E) 9.16×10^-4 N·m

51. During ventricular fibrillation, the myocardial cells do not stop beating; instead, they fall into a state of extreme chaos and rapid twitching, which the heart cannot pump blood effectively. An Automated External Defibrillator (AED) acts to reboot the heart by forcing a powerful electric current through it. The AED must generate high voltage to deliver a current of approximately 20 Amperes into the body within a short duration of about 0.01 seconds. The energy setting for a modern AED is 300 Joules. Estimate the voltage V required for this device and the average chest wall impedance R during a shock. Assuming all processes satisfy Ohm's Law. (A) 2100 Volt, 105 Ohm (B) 1900 Volt, 90 Ohm (C) 1700 Volt, 85 Ohm (D) 1500 Volt, 75 Ohm (E) 1300 Volt, 65 Ohm

52. Which of the following is not a fundamental characteristic of laser light? (A) high monochromaticity (B) high energy conversion efficiency (C) high collimation (D) high directionality (E) high coherence

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

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