8.S: Atomic Structure (Summary)
 Page ID
 10321
Key Terms
angular momentum orbital quantum number (l)  quantum number associated with the orbital angular momentum of an electron in a hydrogen atom 
angular momentum projection quantum number (m)  quantum number associated with the zcomponent of the orbital angular momentum of an electron in a hydrogen atom 
atomic orbital  region in space that encloses a certain percentage (usually 90%) of the electron probability 
Bohr magneton  magnetic moment of an electron, equal to \(\displaystyle 9.3×10^{−24}J/T\) or \(\displaystyle 5.8×10^{−5}eV/T\) 
braking radiation  radiation produced by targeting metal with a highenergy electron beam (or radiation produced by the acceleration of any charged particle in a material) 
chemical group  group of elements in the same column of the periodic table that possess similar chemical properties 
coherent light  light that consists of photons of the same frequency and phase 
covalent bond  chemical bond formed by the sharing of electrons between two atoms 
electron configuration  representation of the state of electrons in an atom, such as \(\displaystyle 1s^22s^1\) for lithium 
fine structure  detailed structure of atomic spectra produced by spinorbit coupling 
fluorescence  radiation produced by the excitation and subsequent, gradual deexcitation of an electron in an atom 
hyperfine structure  detailed structure of atomic spectra produced by spinorbit coupling 
ionic bond  chemical bond formed by the electric attraction between two oppositely charged ions 
laser  coherent light produced by a cascade of electron deexcitations 
magnetic orbital quantum number  another term for the angular momentum projection quantum number 
magnetogram  pictoral representation, or map, of the magnetic activity at the Sun’s surface 
metastable state  state in which an electron “lingers” in an excited state 
monochromatic  light that consists of photons with the same frequency 
Moseley plot  plot of the atomic number versus the square root of Xray frequency 
Moseley’s law  relationship between the atomic number and Xray photon frequency for Xray production 
orbital magnetic dipole moment 
measure of the strength of the magnetic field produced by the orbital angular momentum of the electron 
Pauli’s exclusion principle  no two electrons in an atom can have the same values for all four quantum numbers \(\displaystyle (n,l,m,ms)\) 
population inversion  condition in which a majority of atoms contain electrons in a metastable state 
principal quantum number (n)  quantum number associated with the total energy of an electron in a hydrogen atom 
radial probability density function  function use to determine the probability of a electron to be found in a spatial interval in r 
selection rules  rules that determine whether atomic transitions are allowed or forbidden (rare) 
spin projection quantum number (\(\displaystyle m_s\))  quantum number associated with the zcomponent of the spin angular momentum of an electron 
spin quantum number (s)  quantum number associated with the spin angular momentum of an electron 
spinflip transitions  atomic transitions between states of an electronproton system in which the magnetic moments are aligned and not aligned 
spinorbit coupling  interaction between the electron magnetic moment and the magnetic field produced by the orbital angular momentum of the electron 
stimulated emission  when a photon of energy triggers an electron in a metastable state to drop in energy emitting an additional photon 
transition metal  element that is located in the gap between the first two columns and the last six columns of the table of elements that contains electrons that fill the d subshell 
valence electron  electron in the outer shell of an atom that participates in chemical bonding 
Zeeman effect  splitting of energy levels by an external magnetic field 
Key Equation
Orbital angular momentum  \(\displaystyle L=\sqrt{l(l+1)}ℏ\) 
zcomponent of orbital angular momentum  \(\displaystyle L_z=mℏ\) 
Radial probability density function  \(\displaystyle P(r)dr=∣ψ_{n00}∣^24πr^2dr\) 
Spin angular momentum  \(\displaystyle S=\sqrt{s(s+1)}ℏ\) 
zcomponent of spin angular momentum  \(\displaystyle S_z=m_sℏ\) 
Electron spin magnetic moment  \(\displaystyle \vec{μ_s}=(\frac{e}{m_e})\vec{S}\) 
Electron orbital magnetic dipole moment  \(\displaystyle \vec{μ}=−(\frac{e}{2m_e})\vec{L}\) 
Potential energy associated with the magnetic interaction between the orbital magnetic dipole moment and an external magnetic field \(\displaystyle vec{B}\)  \(\displaystyle U(θ)=−μ_zB=mμ_BB\) 
Maximum number of electrons in a subshell of a hydrogen atom  \(\displaystyle N=4l+2\) 
Selection rule for atomic transitions in a hydrogenlike atom  \(\displaystyle Δl=±1\) 
Moseley’s law for Xray production  \(\displaystyle (Z−1)=constant\sqrt{f}\) 
Summary
8.1 The Hydrogen Atom

A hydrogen atom can be described in terms of its wave function, probability density, total energy, and orbital angular momentum.

The state of an electron in a hydrogen atom is specified by its quantum numbers (n, l, m).

In contrast to the Bohr model of the atom, the Schrödinger model makes predictions based on probability statements.

The quantum numbers of a hydrogen atom can be used to calculate important information about the atom.
8.2 Orbital Magnetic Dipole Moment of the Electron

A hydrogen atom has magnetic properties because the motion of the electron acts as a current loop.

The energy levels of a hydrogen atom associated with orbital angular momentum are split by an external magnetic field because the orbital angular magnetic moment interacts with the field.

The quantum numbers of an electron in a hydrogen atom can be used to calculate the magnitude and direction of the orbital magnetic dipole moment of the atom.
8.3 Electron Spin

The state of an electron in a hydrogen atom can be expressed in terms of five quantum numbers.

The spin angular momentum quantum of an electron is = \(\displaystyle +½\). The spin angular momentum projection quantum number is \(\displaystyle m_{s} =+½\) or \(\displaystyle −½\) (spin up or spin down).

The fine and hyperfine structures of the hydrogen spectrum are explained by magnetic interactions within the atom.
8.4 The Exclusion Principle and the Periodic Table

Pauli’s exclusion principle states that no two electrons in an atom can have all the same quantum numbers.

The structure of the periodic table of elements can be explained in terms of the total energy, orbital angular momentum, and spin of electrons in an atom.

The state of an atom can be expressed by its electron configuration, which describes the shells and subshells that are filled in the atom.
8.5 Atomic Spectra and Xrays

Radiation is absorbed and emitted by atomic energylevel transitions.

Quantum numbers can be used to estimate the energy, frequency, and wavelength of photons produced by atomic transitions.

Atomic fluorescence occurs when an electron in an atom is excited several steps above the ground state by the absorption of a highenergy ultraviolet (UV) photon.

Xray photons are produced when a vacancy in an inner shell of an atom is filled by an electron from the outer shell of the atom.

The frequency of Xray radiation is related to the atomic number Z of an atom.
8.6 Lasers

Laser light is coherent (monochromatic and “phase linked”) light.

Laser light is produced by population inversion and subsequent deexcitation of electrons in a material (solid, liquid, or gas).

CD and BluRay players uses lasers to read digital information stored on discs.
Contributors
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).