[Levine chapter 6] a) For an electron in the ground-state of an H atom, what is r ? b) Repeat (a) for 1/r, but do it without doing an integral. How is 1/r related to this? Explain any similarities or differences. c) What is the most likely distance from the nucleus at which you will find the electron? d) Within what radius is there exactly a 90% chance of finding the electron? Make a plot of the radial distribution function, and mark all the different separations found in (a)-(d), explaining their order in terms of the shape of the plot. e) How many nodes does a 3px orbital have, and which are angular and which are radial? f) How much energy is needed to ionize an H atom in the 3d state? g) Explain why there are exactly 14f electrons. h) What is the energy and degeneracy of the level containing the 35 th excited state of H ? i) In He+, one of the protons instantly becomes a neutron. What fraction of the electron is still in the ground state? Plot both relevant radial probability densities and rationalize your result. j) Give a formula for transition frquencies out of the ground-state of He+