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

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

Coulomb potential energy of an electron in a hydrogenic atom

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

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 energy (I)

The minimum energy required to remove an electron from the ground state, the state of lowest energy, of one of its atoms

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 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

Transition

When an electron moves from a higher energy orbital to a lower energy orbital

Selection rule

A statement about which transitions are allowed

Grotrian diagram

It summarizes the energies of the states and the transitions between the selection rules and atomic energy levels

Orbital approximation

Its when we suppose that a reasonable first approximation to this exact wavefunction is obtained by thinking of each electron as occupying its "own" orbital

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

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

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

Potential energy of the electrons

Quantum defect

An empirical quantity

Rydberg 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

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 of a spectrum

The structure in a spectrum due to spin-orbit coupling

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.

Total orbital angular momentum quantum number (L)

It tells us the magnitude of the angular momentum

Multiplicity of a term

The value of 2S + 1, where S is the total spin quantum number

Clebsch-Gordan series

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