El Eh ]. Trapped in the Nucleus [ll] pts} The average size of the nuclei in atoms is on the order of lllr\" to. while the average size of an atom is typically about It]? to. a. For a particle to be conned in the nucleus, its dc Broglie wavelength needs to be comparable to the size of the nucleus. From this fact, what do you estimate the speed of an electron conned in the nucleus would be? {For simplicity. you may use the nonrelativistic formula for momentum here, but comment on whether your answer would be signicantly affected if you used the full relativistic formula.) b. How would your answer be changed if you used the Heisenberg Uncertainty Principle instead? c. Given your estimate of speed from part a, what would be the electron*s kinetic energy? Written Homework Set #12 Quantum Mechanics || pg. 2 of 3 Due: 1 1 :59 pm. Wednesday. April 2E. 223 d. Estimate the electrostatic potential energy of an electron confined somehow to the nucleus of an atom whose nucleus has 2' protons. This is only an estimate. so you do not need to average over positions in a uniformly charged sphere with an integral, like you might have done in PHYS 152. e. For an in versesquare force law {such as Coulomb attraction] the average potential energy ofa system will be twice as large as the average kinetic energy [and ofthe opposite sign. of course]. 1What does this tell you about the likelihood of nding an electron confined inside the nucleus. f. Suppose the electron had the same mass as a proton. How would this affect your answers to parts c and e above