{"id":238,"date":"2019-04-09T01:42:44","date_gmt":"2019-04-09T05:42:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/?post_type=chapter&p=238"},"modified":"2019-04-10T14:40:49","modified_gmt":"2019-04-10T18:40:49","slug":"chapter-4-review","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/chapter\/chapter-4-review\/","title":{"raw":"Chapter 4 Review","rendered":"Chapter 4 Review"},"content":{"raw":"
\r\n

Key Terms<\/span><\/h3>\r\n
\r\n \t
angular momentum orbital quantum number (l<\/em>)<\/dt>\r\n \t
quantum number associated with the orbital angular momentum of an electron in a hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
angular momentum projection quantum number (m<\/em>)<\/dt>\r\n \t
quantum number associated with the\u00a0<\/span>z<\/em>-component of the orbital angular momentum of an electron in a hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
atomic orbital<\/dt>\r\n \t
region in space that encloses a certain percentage (usually 90%) of the electron probability<\/dd>\r\n<\/dl>\r\n
\r\n \t
Bohr magneton<\/dt>\r\n \t
magnetic moment of an electron, equal to\u00a0<\/span>9.3\u00d710\u221224J\/T<\/span><\/span><\/span>\u00a0<\/span>or\u00a0<\/span>5.8\u00d710\u22125eV\/T<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
braking radiation<\/dt>\r\n \t
radiation produced by targeting metal with a high-energy electron beam (or radiation produced by the acceleration of any charged particle in a material)<\/dd>\r\n<\/dl>\r\n
\r\n \t
chemical group<\/dt>\r\n \t
group of elements in the same column of the periodic table that possess similar chemical properties<\/dd>\r\n<\/dl>\r\n
\r\n \t
coherent light<\/dt>\r\n \t
light that consists of photons of the same frequency and phase<\/dd>\r\n<\/dl>\r\n
\r\n \t
covalent bond<\/dt>\r\n \t
chemical bond formed by the sharing of electrons between two atoms<\/dd>\r\n<\/dl>\r\n
\r\n \t
electron configuration<\/dt>\r\n \t
representation of the state of electrons in an atom, such as\u00a0<\/span>1s22s1<\/span><\/span><\/span>\u00a0<\/span>for lithium<\/dd>\r\n<\/dl>\r\n
\r\n \t
fine structure<\/dt>\r\n \t
detailed structure of atomic spectra produced by spin-orbit coupling<\/dd>\r\n<\/dl>\r\n
\r\n \t
fluorescence<\/dt>\r\n \t
radiation produced by the excitation and subsequent, gradual de-excitation of an electron in an atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
hyperfine structure<\/dt>\r\n \t
detailed structure of atomic spectra produced by spin-orbit coupling<\/dd>\r\n<\/dl>\r\n
\r\n \t
ionic bond<\/dt>\r\n \t
chemical bond formed by the electric attraction between two oppositely charged ions<\/dd>\r\n<\/dl>\r\n
\r\n \t
laser<\/dt>\r\n \t
coherent light produced by a cascade of electron de-excitations<\/dd>\r\n<\/dl>\r\n
\r\n \t
magnetic orbital quantum number<\/dt>\r\n \t
another term for the angular momentum projection quantum number<\/dd>\r\n<\/dl>\r\n
\r\n \t
magnetogram<\/dt>\r\n \t
pictoral representation, or map, of the magnetic activity at the Sun\u2019s surface<\/dd>\r\n<\/dl>\r\n
\r\n \t
metastable state<\/dt>\r\n \t
state in which an electron \u201clingers\u201d in an excited state<\/dd>\r\n<\/dl>\r\n
\r\n \t
monochromatic<\/dt>\r\n \t
light that consists of photons with the same frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
Moseley plot<\/dt>\r\n \t
plot of the atomic number versus the square root of X-ray frequency<\/dd>\r\n<\/dl>\r\n
\r\n \t
Moseley\u2019s law<\/dt>\r\n \t
relationship between the atomic number and X-ray photon frequency for X-ray production<\/dd>\r\n<\/dl>\r\n
\r\n \t
orbital magnetic dipole moment<\/dt>\r\n \t
measure of the strength of the magnetic field produced by the orbital angular momentum of the electron<\/dd>\r\n<\/dl>\r\n
\r\n \t
Pauli\u2019s exclusion principle<\/dt>\r\n \t
no two electrons in an atom can have the same values for all four quantum numbers\u00a0<\/span>(n,l,m,ms)<\/span><\/span><\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
population inversion<\/dt>\r\n \t
condition in which a majority of atoms contain electrons in a metastable state<\/dd>\r\n<\/dl>\r\n
\r\n \t
principal quantum number (n<\/em>)<\/dt>\r\n \t
quantum number associated with the total energy of an electron in a hydrogen atom<\/dd>\r\n<\/dl>\r\n
\r\n \t
radial probability density function<\/dt>\r\n \t
function use to determine the probability of a electron to be found in a spatial interval in\u00a0<\/span>r<\/em><\/dd>\r\n<\/dl>\r\n
\r\n \t
selection rules<\/dt>\r\n \t
rules that determine whether atomic transitions are allowed or forbidden (rare)<\/dd>\r\n<\/dl>\r\n
\r\n \t
spin projection quantum number (ms<\/span><\/span><\/span>)<\/dt>\r\n \t
quantum number associated with the\u00a0<\/span>z<\/em>-component of the spin angular momentum of an electron<\/dd>\r\n<\/dl>\r\n
\r\n \t
spin quantum number (s<\/em>)<\/dt>\r\n \t
quantum number associated with the spin angular momentum of an electron<\/dd>\r\n<\/dl>\r\n
\r\n \t
spin-flip transitions<\/dt>\r\n \t
atomic transitions between states of an electron-proton system in which the magnetic moments are aligned and not aligned<\/dd>\r\n<\/dl>\r\n
\r\n \t
spin-orbit coupling<\/dt>\r\n \t
interaction between the electron magnetic moment and the magnetic field produced by the orbital angular momentum of the electron<\/dd>\r\n<\/dl>\r\n
\r\n \t
stimulated emission<\/dt>\r\n \t
when a photon of energy triggers an electron in a metastable state to drop in energy emitting an additional photon<\/dd>\r\n<\/dl>\r\n
\r\n \t
transition metal<\/dt>\r\n \t
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\u00a0<\/span>d<\/em>\u00a0<\/span>subshell<\/dd>\r\n<\/dl>\r\n
\r\n \t
valence electron<\/dt>\r\n \t
electron in the outer shell of an atom that participates in chemical bonding<\/dd>\r\n<\/dl>\r\n
\r\n \t
Zeeman effect<\/dt>\r\n \t
splitting of energy levels by an external magnetic field<\/dd>\r\n<\/dl>\r\n<\/div>\r\n
\r\n

Key Equations<\/span><\/h3>\r\n
\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Orbital angular momentum<\/td>\r\nL=l(l+1)\u210f<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
z<\/em>-component of orbital angular momentum<\/td>\r\nLz=m\u210f<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Radial probability density function<\/td>\r\nP(r)dr=|\u03c8n00|24\u03c0r2dr<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Spin angular momentum<\/td>\r\nS=s(s+1)\u210f<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
z<\/em>-component of spin angular momentum<\/td>\r\nSz=ms\u210f<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Electron spin magnetic moment<\/td>\r\n\u03bc\u2192s=(eme)S\u2192<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Electron orbital magnetic dipole moment<\/td>\r\n\u03bc\u2192=\u2212(e2me)L\u2192<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Potential energy associated with the magnetic\r\n<\/span>interaction between the orbital magnetic dipole\r\n<\/span>moment and an external magnetic field\u00a0<\/span>B\u2192<\/span><\/span><\/span><\/td>\r\nU(\u03b8)=\u2212\u03bczB=m\u03bcBB<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Maximum number of electrons in a subshell of\r\n<\/span>a hydrogen atom<\/td>\r\nN=4l+2<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Selection rule for atomic transitions in a\r\n<\/span>hydrogen-like atom<\/td>\r\n\u0394l=\u00b11<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n
Moseley\u2019s law for X-ray production<\/td>\r\n(Z\u22121)=constantf<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n

Summary<\/span><\/h3>\r\n
\r\n
\r\n

4.1<\/span>\u00a0<\/span><\/span>The Hydrogen Atom<\/span><\/a><\/h4>\r\n