A. Particle in a one-dimensional box. 1. Using the equation for the particle in the one-dimensional well. Calculate the difference of energy between energy levels n = 2 and n = 3 as well as the l of the photon capable of introducing this transition considering the following systems: a) An electron moving in a box of a = 2 cm b) An electron moving in a box of a = 6 cm c) A marble of m = 1g moving in a box of a = 6 cm 2. Determine the allowed energies for a one-dimensional potential box in a energy diagram for levels n = 1-8 considering a = 1 . B. Particle in a two-dimensional box. 3. Consider for 8e-, a 2-dimensional potential box with a = 4 and determine what following: a) Calculate the energy required for the most probable transition. b) Yes, the square is distorted to a rectangle with sides a = 2 and b = 8 . Which of the two boxes will be the most stable? c) Calculate what measures the rectangle must be so that it has the same energy as the square. Considering that a = 2b. d) Yes, I change the box and I have a 3D box for the 8e- What will be the maximum length of transition? C. Particle in a three-dimensional box. eje z y=00 i VO eje x 4.-Suppose that we have a proton confined within a cubic box with side L = 1m. Calculate the number of stationary energy levels (including degeneration) with energy S 1 MeV contained in the box