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Unformatted text preview: CHEMISTRY 201X: Homework #5 Due : Monday, October 15, 2007 -1- Wavefunctions and Electronic Transitions (1) (8 pts) Using the Bohr model for the hydrogen atom, (a) (2 pts) Derive an expression for the speed v n of an electron in orbit n in terms of h , m , and e , where h is Plancks constant, m and e are the mass and charge of the electron. (b) (2 pts) Calculate the speed (in m/sec) of an electron in the ground state and the two lowest excited states of the H atom. (c) (2 pts) In a transition from the ground state of H that involves moving an electron through a distance that is approximately equal to the orbit diameter of the ground state, what characteristic time would be required for the transition? (d) (2 pts) How does this time compare with the time required for the H atom to move the same distance at its root-mean-square speed? (2) (24 pts) An important model to describe electronic states in chemical systems (molecules and solids) is the particle-in-a-box model, in which the electronic wavefunctions are completely...
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