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

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Presentation on theme: "Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 16 The Particle in the Box and the Real World."— Presentation transcript:

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

2 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World Objectives Importance of the concept for particle in the box Understanding the tunneling of quantum mechanical particles

3 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World Outline 1.The Particle in the Finite Depth Box 2.Differences in Overlap between Core and Valence Electrons 3.Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box 4.Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator?

4 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World Outline 5.Tunneling through a Barrier 6.The Scanning Tunneling Microscope 7.Tunneling in Chemical Reactions

5 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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,

6 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

7 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

8 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

9 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 16.5 Tunneling through a Barrier Consider a particle with energy E confined to a very large box. A barrier of height V 0 separates two regions in which E < V 0. The particle can escape the barrier and go over the barrier, called tunneling.

10 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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

11 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

12 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 16.6 The Scanning Tunneling Microscope Scanning Tunneling Microscope (STM)

13 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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

14 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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?

15 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

16 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

17 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 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.

18 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 16: The Particle in the Box and the Real World 16.6 The Scanning Tunneling Microscope


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