(BQ) Part 1 book "Physical chemistry" has contents: The Electronic structure of polyatomic molecules, the electronic structure of polyatomic molecules; translational, rotational, and vibrational states of atoms and molecules, optical spectroscopy and photochemistry; magnetic resonance spectroscopy,and other contents. | 17 The Electronic States of Atoms. I. The Hydrogen Atom PRINCIPAL FACTS AND IDEAS 1. The hydrogen atom is an example of a central-force system (a two-particle system in which the potential energy depends only on the distance between the two particles). 2. The Schrödinger equation for the hydrogen atom can be separated into one equation for the motion of the center of mass and one equation for the motion of the electron relative to the nucleus. 3. The relative Schrödinger equation can be solved in spherical polar coordinates by separation of variables, assuming that ψ R(r)Θ(θ)Φ(φ). These wave functions are called orbitals. 4. The energy eigenvalues for the relative motion are the same as in the Bohr theory. 5. The square of the orbital angular momentum of the electron and one component of this angular momentum can have predictable values if a hydrogen atom is in a state corresponding to an energy eigenfunction. The angular momentum values are different from the Bohr theory. 6. Electrons have intrinsic (spin) angular momentum in addition to the angular momentum of orbital motion. 725 726 17 The Electronic States of Atoms. I. The Hydrogen Atom z ze zn xe xn Electron Nucleus (proton) yn ye The Hydrogen Atom and the Central Force System The hydrogen atom is one of the few systems for which the Schrödinger equation can be solved. It consists of a single electron with mass me and charge −e and a nucleus consisting of a single proton with mass mn and charge e , as depicted in Figure . We first assume that the atom is not confined in any container. Its potential energy depends only on the distance between the particles and is given by Coulomb’s law, for which the potential energy is given in Eq. (): V (r) y x Figure The Hydrogen Atom System Consisting of a Nucleus and an Electron. − e2 4πε0 r () where ε0 is the permittivity of the vacuum, and where r is the distance between the nucleus and the electron. This formula corresponds
