Physical Chemistry 2nd Edition Chapter 16 The Particle in the Box and the Real World Physical Chemistry 2nd Edition Thomas Engel, Philip Reid

Objectives Importance of the concept for particle in the box Understanding the tunneling of quantum mechanical particles

Outline The Particle in the Finite Depth Box Differences in Overlap between Core and Valence Electrons Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator?

Outline Tunneling through a Barrier The Scanning Tunneling Microscope Tunneling in Chemical Reactions

16.1 The Particle in the Finite Depth Box For a box to be more realistic, we let the box to have a finite depth. The potential is defined by Outside the box,

16.2 Differences in Overlap between Core and Valence Electrons 16.1 Energy Eigenfunctions and Eigenvalues for a Finite Depth Box Strongly bound levels correspond to core electrons and weakly bound levels correspond to valence electrons.

16.3 Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box The absorption of light in UV of electromagnetic spectrum is due to excitation of electrons. If electrons are delocalized in an organic molecule with a π-bonded network, the absorption spectrum shifts from UV into visible range. Greater the degree of delocalization, the more absorption maximum shifts toward the red end of the visible spectrum.

16.4 Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator? Valence electrons on adjacent atoms in a molecule or a solid can have an overlap. The energy required to remove an electron from the highest occupied state is the work function, ø.

16.5 Tunneling through a Barrier Consider a particle with energy E confined to a very large box. A barrier of height V0 separates two regions in which E < V0. The particle can escape the barrier and go over the barrier, called tunneling.

16.5 Tunneling through a Barrier To investigate tunneling, finite depth box is modified by having a finite thickness. The potential is now where a = barrier width

16.6 The Scanning Tunneling Microscope 16.2 Tunneling through a Barrier Scanning Tunneling Microscope (STM) allows the imaging of solid surfaces with atomic resolution with a surprisingly minimal mechanical complexity. The STM is used to study the phenomena at near atomic resolution.

16.6 The Scanning Tunneling Microscope Scanning Tunneling Microscope (STM)

Example As was found for the finite depth well, the wave function amplitude decays in the barrier according to . This result will be used to calculate the sensitivity of the scanning tunneling microscope. Assume that the tunneling current through a barrier of width a is proportional

Example a. If is 4.50 eV, how much larger would the current be for a barrier width of 0.20 nm than for 0.30 nm? b. A friend suggests to you that a proton tunneling microscope would be equally effective as an electron tunneling microscope. For a 0.20-nm barrier width, by what factor is the tunneling current changed if protons are used instead of electrons?

Solution a. Putting the numbers into the formula given, we obtain Even a small distance change results in a substantial change in the tunneling current.

Solution b. We find that the tunneling current for protons is appreciably smaller than that for electrons. This result does not make the proton tunneling microscope look very promising.

16.6 The Scanning Tunneling Microscope Most chemical reactions proceed faster as the temperature of the reaction mixture is increased. This is due to energy barrier which must be overcome in order to transform reactants into products. This barrier is referred to as the activation energy for the reaction.

16.6 The Scanning Tunneling Microscope