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Photoelectron imaging as a quantum chemistry visualization tool

An overview and simple example of photoelectron imaging is presented, highlighting its efficacy as a pedagogical tool for visualizing quantum phenomena. Specifically, photoelectron imaging of H (the simplest negative ion) is used to demonstrate several quantum mechanical principles. This example could be incorporated into anintroductory quantum chemistry course to extend the traditional discussion of the photoelectric effect and photoelectron spectroscopy into the area of matter waves. In working through this example, several core quantum-mechanical topics and concepts have been explored, such as conservation angular momentum, the transition dipole moment, components of the hydrogenic orbitals, the Born interpretation ofthe wave function, and theory of quantum measurement.
Quantum Chemistry is a daunting subject to many undergraduate students, in part because the underlying principles and concepts can be abstract and difficult to relate to. It has been proposed that modern experimental examples can help to ground quantum theory in clearly observable phenomena and thus facilitate learning. The emerging techniqueof photoelectron imaging can supply such examples. A pedagogical introduction to the technique is provided, aimed at chemical educators and undergraduate students studying physical chemistry. The goal is to provide a contemporary phenomenological means for connecting concepts in quantum theory to experimental results. Some cases where photoelectron imaging might offer a valuable, alternativeillustration of key ideas are highlighted. This approach will also raise awareness of this increasingly important experimental technique in a wider audience.
INTRODUCTION TO PHOTOELECTRON IMAGING
The photoelectric effect is usually discussed in physical chemistry course as part of the introduction to wave-particle duality and the quantization of light. This phenomenon of electron release uponradiation of a metal surface has characteristics that cannot be explained by classical physics. First, increasing the light’s intensity increases the number of electrons released, contrary to the classical expectation that it should increase the speed with which they depart. On the other hand, increasing the frequency of the radiation does increase the speed (or kinetic energy) with which the electronsare ejected and the classical expectation that there should be an increase in the number of electrons released is not realized. Finally, decreasing the frequency to a certain point (unique to the type metal) causes the electron emission to cease, regardless of the light’s intensity.
These observations necessitate a description of light as having both particle and wave-like attributes. Lightindivisible beyond discrete packets, now called photons, each with energy defined by the light’s frequency. The photoelectric effect was explained by Albert Einstein in one of the papers of his annus mirabilis, as a one-photon’s energy is spent in overcoming the binding force, with the excess cinverted into kinetic energy of the released electron (or “photoelectron”). For photons whose energy above thecutoff frequency, electrons may be liberated with kinetic energy (eKE) of
Eke≤ hv-Ф
Where Ф, the work function of the metal, is the smallest photon energy for which photoemission may occur. The photoelectric effect is the most commonly used classroom example of the quantization of light energy.
Applying the light source to atoms and molecules also reveals quantized energy levels in matter.Photoelectron spectroscopy has become an extremely useful and versatile tool for probing the energies of atomic and molecular orbitals. This is usually done through interpretation of the photoelectron energy spectrum, which indicates the probability of the emitted electrons having a certain kinetic energy. The photoelectron spectrum contains the probability of removal of an electron from a given...