Chapter 10 - Atomic Structure and Atomic Spectra

• Electronic structure of an atom - The arrangement of electrons around a nucleus.
• Hydrogenic atom - A one-electron atom or ion of general atomic number Z.
• Many-electron atom (Polyelectronic atom) - An atom or ion with more than one electron.

The structure and spectra of hydrogenic atoms

• Rydberg constant for the hydrogen atom - RH = 109677 cm^-1
• Ritz combination principle - States that the wavenumber of any spectral line is the difference between two terms.

10.1 The structure of hydrogenic atoms

• Radial wave equation

  

• Bohr radius - It is called like this because the same quantity appeared in Bohr's early model of the hydrogen atom as the radius of the electron orbit of lowest energy.

10.2 Atomic orbitals and their energies

• Atomic orbital - A one-electron wavefunction for an electron in an atom.
• Principal quantum number (n) - It can take the values n = 1, 2, 3, … and determines the energy of the electron.
• Bound states of the atom - Where the energy of the atom is lower than that of the infinitely separated, stationary electron and nucleus.
• Unbound states of the electron - The states to which an electron is raised when it is ejected from the atom by a high-energy collision or photon.

Ionization energies

• Ionization energy (I) - The minimum energy required to remove an electron from the ground state, the state of lowest energy, of one of its atoms.

Shells and subshells

• Shell - All the orbitals of a given value of n.
• Subshell - The orbitals with the same value of n but different values of l.
  • Angular momentum quantum number (l) - Depends on the principal quantum number.

Radial distribution functions

• Radial distribution function P(r) - A probability density in the sense that, when it is multiplied by dr, it gives the probability of finding the electron anywhere between the two walls of a spherical shell of thickness dr at the radius r.

10.3 Spectroscopic transitions and selection rules

• Transition - When an electron moves from a higher energy orbital to a lower energy orbital. Some transitions are allowed while others are forbidden.
• Selection rule - A statement about which transitions are allowed. They are derived for atoms by identifying the transitions that conserve angular momentum when a photon is emitted or absorbed.
• Grotrian diagram - It summarizes the energies of the states and the transitions between the selection rules and atomic energy levels.

The structures of many-electron atoms

10.4 The orbital approximation

• Orbital approximation - It’s when we suppose that a reasonable first approximation to this exact wavefunction is obtained by thinking of each electron as occupying its 'own' orbital.

The Pauli principle

• Pauli exclusion principle - No more than two electrons may occupy any given orbital, and if two do occupy one orbital, then their spins must be paired.
• Pauli principle - When the labels of any two identical fermions are exchanged, the total wavefunction changes sign; when the labels of any two identical bosons are exchanged, the total wavefunction retains the same sign.
• Slater determinant - Any acceptable wavefunction for a closed-shell species.
• Valence electrons - The electrons in the outermost shell of an atom in its ground state.

The building-up principle

• Building-up principle - It says that the order of occupation is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s.
• Hund's maximum multiplicity rule - An atom in its ground state adopts a configuration with the greatest number of unpaired electrons.

Ionization energies and electron affinities

• First ionization energy - The minimum energy necessary to remove an electron from a many-electron atom in the gas phase.
• Second ionization energy - The minimum energy needed to remove a second electron from the cation.
• Electron affinity - The energy released when an electron attaches to a gas-phase atom.

10.5 Self-consistent field orbitals

• Potential energy of the electrons

  

The spectra of complex atoms

10.6 Quantum defects and ionization limits

• Quantum defect - An empirical quantity.

• Rydberg states

  

10.7 Singlet and triplet states

• Singlet - The paired-spin arrangement.
• Triplet - The resulting state when the angular momenta of two parallel spins add together to give a nonzero total spin.

10.8 Spin-orbit coupling

• Spin-orbit coupling - The interaction of the spin magnetic moment with the magnetic field arising from the orbital angular momentum.
• Spin-orbit coupling constant - The dependence of the spin-orbit interaction on the value of j.

Fine structure

• Fine structure of a spectrum - The structure in a spectrum due to spin-orbit coupling.

10.9 Term symbols and selection rules

A term symbol gives three pieces of information:

• The letter (P or D in the examples) indicates the total orbital angular momentum quantum number, L.
• The left superscript in the term symbol (the 2 in P^2) gives the multiplicity of the term.
• The right subscript on the term symbol (the 3/2 in P_3/2) is the value of the total angular momentum quantum number, J.

The total orbital anqular momentum

• Total orbital angular momentum quantum number (L) - It tells us the magnitude of the angular momentum.

• Clebsch-Gordan series

  

The multiplicity

• Multiplicity of a term - The value of 2S + 1, where S is the total spin quantum number.
• Russell-Saunders coupling - This scheme is based on the view that, if the spin-orbit coupling is weak, then it is effective only when all the orbital momenta are operating cooperatively.