CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA

CHEMISTRY 312 - HOMEWORK #1

From McQuarrie, Quantum Chemistry Problems: Chapter 1: 2, 7, 8, 12, 20 and 22

Chapter 2: 4, 6, 16 Additional Problems: The relationship between the magnitude of the momentum and the wavelength of a quantum particle is expressed as follows:

�

p = h

!

The momentum of a particle is often written in the following form:

�

p = !k ,

where k is call the wavevector. The wavevector is related to the wavelength of a quantum particle in the following fashion:

�

h

! = !k =

hk

2" # k =

2"

!

When particles have a wavelength this is about the same as the spacing between atoms in a crystal lattice, they can diffract from the lattice and produce an interference pattern. The wavevector of particles that are diffracted by a crystal lattice is k ~ 1Å-1. One is often interested in the dispersion relation, which is the functional dependence relating the wavevector of a particle to its energy, i.e., E(k). Plot the dispersion relations for a photon, an electron, a neutron, and a helium atom versus k in the range 0-10Å-1, and express the energy of the particles in electron volts (eV). That is, make plots with the following axes:

0 2 4 6 8 10 k (Å-1)