HW_2.pdf - ChE 554 HW 2 Due Sunday:59 pm E Term 2020 1 Answer the following questions a Explain the failings of classical mechanics in

HW_2.pdf - ChE 554 HW 2 Due Sunday:59 pm E Term 2020 1...

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ChE 554 E Term 2020 HW 2 Due: Sunday May 31, 11:59 pm 1. Answer the following questions. a. Explain the failings of classical mechanics in describing/modeling atoms, electrons, and molecules. b. Explain what the wavefunction of an atom/molecule is. c. Explain what an eigenvalue and eigenfunction are. d. Explain what the Hamiltonian operator is. e. Explain what a “particle in a box” is. 2. Answer the following questions. a. Describe the experimental results that led to quantum mechanics. b. Describe how to get the measured value (e.g. temperature or momentum) from a wavefunction. c. Explain what atomic units are. d. Explain why an electron around a proton nucleus doesn’t collapse into the nucleus. 3. If ࠵? = ࠵? $ ࠵? , find g for each of the following ࠵? $ and f. Also indicate which solutions are an eigenvalue/eigenfunction. a. ࠵? $ = ࠵?/࠵?࠵? , f = cos(-x) b. ࠵? $ = ࠵? ) /࠵?࠵? ) , f = cos(-x) c. ࠵? $ = ( ) ) , f = sin(x) d. ࠵? $ = ࠵?࠵?࠵? , f = ln(x) 4. Write out the exact wavefunction for the 2p orbitals of a hydrogen atom. Draw/sketch the electron density that would be derived from these wavefunctions.
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