homework_7_2009 - Chem 110A Homework 7: Due MONDAY,...

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Chem 110A Homework 7: Due MONDAY, November 23 Chemistry 110A — 2009 Professor McCurdy 1. Atomic units: (a) Using atomic units, for the quantities in the general formula for the energy levels of a one electron atom, E n = ! Z 2 2 n 2 me 4 16 " 2 # 0 2 ! 2 $ % & ( ) , show that the energy of the helium ion in its ground state in atomic units is -2. These energy units are hartrees. What is that energy in electron volts? (b) The “fine structure” constant is a unitless constant defined in terms of other elementary physical constants as: ! = e 2 ! c 4 "# 0 = 1 137.035999 (to 9 significant digits). Using this definition, express the quantities in the fine structure constant in atomic units, and thus show that in atomic units the speed of light is c = 137.0 (to 4 figures). The units are a 0 /(atomic time units). (c) Since the speed of light has to have units of length/time, use the fact that the Bohr radius a 0 = 5.2918 x 10 -11 m and the value of c in SI units (2.9979 x 10 -10 m/sec) to express the atomic unit of time in seconds. The period of the first Bohr orbit is 2 in atomic units. If you did part (c) correctly you should find that 2 times the atomic unit time in seconds is about 150 attoseconds = 150 x 10 -18 s. It is now possible to make pulses of ultraviolet light that last only 250 attoseconds. It’s instructive to read this short abstract of an article in Nature in 2004 (volume 427, page 817) reporting the results of the first experiments with 250 attosecond pulses. This work is what a Nobel prize looks like before it is won.
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homework_7_2009 - Chem 110A Homework 7: Due MONDAY,...

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