Problem Set 1 CHEM 562 Due date: March 6, 2020 Problem 1. Read the textbook, chapter XXXXXXXXXX. Problem 2. Compute the wavelength, frequency, and wavenumber of the n = 5 → n = 4 transition in Li2+....

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Problem Set 1 CHEM 562 Due date: March 6, 2020 Problem 1. Read the textbook, chapter 9.1-9.5. Problem 2. Compute the wavelength, frequency, and wavenumber of the n = 5 → n = 4 transition in Li2+. Problem 3. When ultraviolet radiation of wavelength 58.4 nm from a helium lamp is di- rected on to a sample of xenon, electrons are ejected with a speed of 1.79 Mm s−1. Calculate the ionization energy of xenon. Problem 4. The wavefunction for the 2s orbital of a hydrogen atom is N (2− r/a0) e−r/2a0 . Determine the normalization constant N . Problem 5. What is the orbital angular momentum of an electron in the orbitals (a) 4d, (b) 2p, (c) 3p? Give the numbers of angular and radial nodes in each case. Problem 6. A series of lines in the spectrum of atomic hydrogen lies at 656.46 nm, 486.27 nm, 434.17 nm, and 410.29 nm. What is the wavelength of the next line in the series? What is the ionization energy of the atom when it is in the lower state of the transitions? Problem 7. An electron in the ground-state He+ ion undergoes a transition to a state described by the wavefunction R4,1 (r)Y1,1 (θ, φ). (a) Describe the transition using term symbols. (b) Compute the wavelength, frequency, and wavenumber of the transition. (c) By how much does the mean radius of the electron change due to the transition? Problem 8. Show that lz and l 2 both commute with the hamiltonian for a hydrogen atom. What is the significance of this result? 1