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.

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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