Chapter 35. The Hydrogen Atom

Arthur Haas

Arthur Haas

P. Anthony Cox

This chapter focuses on the hydrogen atom, which is the most important chemical application of the quantum theory. The hydrogen atom was Erwin Schrödinger's immediate goal when he developed his equation, and the solution obtained in 1926 persuaded him and indeed most interested physicists that his theory was successful. Indeed, the solutions of Schrödinger's equation — known as atomic orbitals — form the basis of our understanding, not only of atomic structure, but also of chemical bonding in molecules and solids. The chapter begins by considering the Rutherford–Bohr atom. It then looks at hydrogenic ions. The solutions described in the chapter are 'exact', in the mathematical sense that they can be obtained from the Schrödinger's equation without approximation. However, they are not quite 'correct', because this equation does not truly describe a real hydrogen atom.

Randell L Mills

Ram Yatan Prasad, Pranita

This chapter begins with the simple solution of the Schrödinger equation for hydrogen atom for which the energy value has been derived. The Bohr radius of H atom has also been computed. After this, this chapter provides the generalised solution of the Schrödinger equation for H atom/hydrogen-like species in which F equation, R equation, and T equations have been derived in a simple and lucid way. This chapter also deals with the Laguerre differential equation, Laguerre polynomials, Rodrigues formula for the Laguerre polynomials, Laguerre associated equation and its solution, associated Laguerre polynomials, Rodrigues formula for the associated Laguerre polynomials, and solution of the radial equation. It also provides normalisation of the radial wave function and complete wave function; for the hydrogen atom, hydrogenic atomic orbital; electron density of 1 s electron; mathematical background of shape of orbitals; the most probable distance of electron from nucleus of hydrogen atom, and average distance of electron from the nucleus of hydrogen atom. The end of this chapter describes the references and adequate computational problems (solved problems and question on concepts).

Akira Hirose, Karl E. Lonngren

This chapter covers the following topics: Photoelectric Effect and Einstein's Photon Theory; Hydrogen Atom and deBroglieWave. Chapter Contents: 13.1 Introduction 13.2 Photoelectric Effect and Einstein's Photon Theory 13.3 Hydrogen Atom 13.4 de Broglie Wave 13.5 Problems Inspec keywords: wave mechanics; photoelectricity; hydrogen; particle optics Other keywords: photoelectric effect; de BroglieWave; Hydrogen Atom; Einstein's Photon Theory Subjects: Atom and neutron optics; Textbooks; Particle beams and particle optics