This chapter examines the hydrogenic atom, which is a one-electron atom or ion of general atomic number Z. It provides a set of concepts which are used to describe the structures of atoms and of molecules. It analyzes the experimental information from a study of the spectrum of atomic hydrogen and describes the results of solving the Schrödinger equation. It also considers the importance of wavefunctions to the atomic orbitals of hydrogenic atoms. The chapter talks about the atomic orbitals which are labelled by quantum numbers that specify the energy and angular momentum of an electron in a hydrogenic atom. It shows the production of energetically excited atoms when an electric discharge is passed through a gas or vapour or when an element is exposed to a hot flame.
This chapter examines the hydrogenic atom, which is a one-electron atom or ion of general atomic number Z. It provides a set of concepts which are used to describe the structures of atoms and of molecules. It analyzes the experimental information from a study of the spectrum of atomic hydrogen and describes the results of solving the Schrödinger equation. It also considers the importance of wavefunctions to the atomic orbitals of hydrogenic atoms. The chapter talks about the atomic orbitals which are labelled by quantum numbers that specify the energy and angular momentum of an electron in a hydrogenic atom. It shows the production of energetically excited atoms when an electric discharge is passed through a gas or vapour or when an element is exposed to a hot flame.
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.
Abstract This chapter reiterates the quantum numbers for atomic orbitals, known from general chemistry, and places them into the context developed so far. It is sketched how the Schrodinger equation (SE) for the hydrogen atom hydrogen-like systems (one electron plus a nucleus of charge Z) is set up. When the nucleus is treated as a fixed point charge, the SE is only for the electron. The solutions of the SE can be obtained by switching to spherical polar coordinates, such that the variables are separable in terms of the electron distance from the nucleus, r, and two angles. The kinetic energy of the electron then has a radial component, and an angular component. The latter is associated with the angular momentum quantum number, which is codified by the letters s, p, d, f, and so forth. A step by step solution of the SE is provided later, in chapter 19.
We begin our study of atomic physics by relying on the phenomenological notions summarized in chapter 1 and by fully exploiting the quantum mechanical formalism outlined in chapter 2. A hierarchy of approximations will be introduced in the first instance to describe the hydrogen atom, which allows one to focus on the main features of its energy spectrum and quantum properties, including the key ‘atomic orbital’ concept. Next, these results will be extended to the more general case of hydrogenic atoms. The physical picture will be made more rigorous by introducing the magnetic interactions, included those linked to the intrinsic spin degree of freedom, leading to the full description of the fine and hyperfine structure of one-electron atoms. The effects of a static external magnetic or electric field will be eventually discussed by calculating the corresponding energy shifts and splittings of the energy levels.
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).
Bohr theory was not satisfactory as it failed to provide an interpretation of relative line intensities and splitting of spectral lines in the presence of electric field and magnetic field in the hydrogen spectrum. This theory also failed completely when it was applied to explain the energies and spectra of more complex atoms. In this chapter, we consider the application of Schrödinger wave theory to one-electron atom. The simplest one-electron system is the Hydrogen atom, whose Schrödinger equation can be exactly solved. Other one-electron system like He + , Li 2+ etc. can also be solved exactly. The chemical system with more than one-electron cannot be solved exactly due to electron-electron repulsion, which is the most problematic term.
Bohr theory was not satisfactory as it failed to provide an interpretation of relative line intensities and splitting of spectral lines in the presence of electric field and magnetic field in the hydrogen spectrum. This theory also failed completely when it was applied to explain the energies and spectra of more complex atoms. In this chapter, we consider the application of Schrodinger wave theory to one-electron atom. The simplest one-electron system is the Hydrogen atom, whose Schrodinger equation can be exactly solved. Other one-electron system like He + , Li 2+ etc. can also be solved exactly. The chemical system with more than one-electron cannot be solved exactly due to electron-electron repulsion, which is the most problematic term.