Chemistry 3730 assignment 6

Due: Friday, Oct. 17, 10:00 a.m.

1. We will soon be studying the harmonic oscillator, a model of a vibrating chemical bond. The ground-state harmonic oscillator wavefunction is of the form

   

   where a is a positive parameter related to the bond stiffness and to the reduced mass of atoms participating in the bond. In this problem, x can range from to . Find the value of A which normalizes the wavefunction.

2. Fluorescence can be used to view the positions of ions in ion traps. Using a technique called laser cooling, Wineland and coworkers reduced the kinetic energies of ions to . They were able to view the ions with a resolution of . The mass of the ion is approximately .
   1. What is the expected fractional change in momentum ( ) which must accompany this measurement?
   2. By how much is the kinetic energy of the ions potentially increased by the measurement? Express your answer as a percentage of the kinetic energy.