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The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 19 (2014) pp 384-389

Pressure-induced Ionization of Hydrogen: A Computational Project

Jonathan Hunt, James Martin, Vanessa Rosing, Josh Winner and Henry E. Montgomery, Jr.*

Chemistry Program, Centre College, 600 West Walnut Street, Danville, KY 40422-1394,
Received October 13, 2014. Accepted November 25, 2014.

Published: 19 December 2014

Abstract. When the pressure on an atom is increased to the megapascal region, the electronic energy increases to the point where spontaneous ionization occurs. Thispressure-induced ionization of hydrogen is an important consideration when modeling the atmosphere of the gas giant planets. This paper describes an undergraduate computational chemistry project that models pressure-induced ionization using a hydrogen atom confined at the center of  a spherical barrier of finite height. This system is exactly solvable in Kummer’s confluent hypergeometric functions and lends itself to treatment using a computer algebra system. Energy quantization results from matching the wave function and its first derivative at the barrier. When the radius of confinement decreases, the electron energy increases. When the electron energy reaches the height of the confining barrier, pressure-induced ionization occurs. Electronic energies were calculated over a range of confinement radii from 1 a0 (53 pm) to 6 a0 (318 pm). The minimum confinement radius necessary to support a bound 1s ground state was calculated for barrier heights from 0 to 100 Eh (2720 eV).

Key Words: Laboratories and Demonstrations; physical chemistry; quantum mechanics; confined atoms; pressure-induced ionization

(*) Corresponding author. (E-mail:

Article in PDF format (114 KB) HTML format

Supporting Materials:

One supporting file with the student poster is available in PowerPoint format (867 KB).

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