Physical Chemistry Third Edition

1376 Index

Probability density (cont.)
for excited state, 773
of harmonic oscillator, 703–704, 703–704f
for helium, 794–795
orbital region, 747
of particle in one-dimensional box,
701–702, 701–702f
of particle in three dimensions, 705
symmetric, 767
for two particles, 769–771
Probability distribution, 385, 394
average, 1043–1044, 1045t
Boltzmann, 942
canonical, 1122–1124
different expression for, 1116–1117
for dilute gas, 1047–1054
average distribution, 1048
most probable distribution, 1048–1054
of gas kinetic theory
derivation of, 395–397, 395f
identification of parameter b, 398–404,
399f, 404f
macrostates and microstates, 384–386
velocity, 394–404
molecular partition function and, 1055–1063
definition of, 1055
of a dilute monatomic gas, 1057–1063,
1059f
parameterαand, 1055–1056
parameterβand, 1056
probability distribution and, 1055–1063
of molecular speeds, 383, 405–410, 437
equation for, 407
mean-square speed, 409
results of, 408, 408f
spherical polar coordinates for,
405–406, 406f
for molecular states, 1043–1046
normalized, 399
standard deviation of, 399–400, 399f
three-dimensional, 403–404, 404f
Probability equations, 700–701
Probability of reaction, in collision theory, 537
Product
concentration, chemical reactions
dependence on, 485
of mathematical group, 898
of two operators, 686
Product partition function, corrections to,
1070–1072
Products of inertia, 933–934

Prolate symmetric top, 934

Protease, 575–576

Proteins, 1197

Proust, Joseph, 4

Pseudo first-order reaction, 504

Pseudo second-order reaction, 504

P-type semiconductor, 1174

Pyruvate kinase, 345–346

q.SeeHeat

Quantum chemistry software, for

computational chemistry, 909–911

Quantum harmonic oscillator, 674–679

Quantum mechanical operator, for mechanical

variables, 689

Quantum mechanics, 619–620

classical mechanicsvs., 620

correspondence principle of, 702

particle encounters, 767

De Broglie waves, 654–656

mathematics used in, 1275–1281

operators of, 688–695

eigenfunction of coordinate, 695

hermitian, 692–694

linear, 692

particle in a box, 663–673

free particle in one dimension, 670–672

free particle in three dimensions,

672–673

one-dimensional, 663–666, 664f

Schrödinger equation and de Broglie

waves, 666–667

specification of state of, 668–669

in three-dimensions, 669–670, 669f,

1276–1278

time-dependent wave function, 668

postulates of, 683–722

fifth, 683, 717–720, 722

first, 683–684, 721

fourth, 683, 696–710, 721–722

second, 683–684, 721

summary for, 721–722

third, 683–695, 721

uncertainty principle of Heisenburg,

711–716

quantum harmonic oscillator, 674–679

Schrödinger equation, 657–663

eigenvalue equations, 662–663

in three dimensions, 661–662

time-dependent, 659–661

time-independent, 658–659

of spectroscopic transitions, 951–955,

954–955f

summary for, 680–681

Quantum numbers, 643, 648, 774

of hydrogen atoms, 739

translational, 916

types of, 739

Quantum statistical mechanics

molecular partition function

calculation of, 1064–1075

probability distribution, 1055–1063

postulates of, 1042–1043

probability distribution

for dilute gas, 1047–1054

molecular partition function, 1055–1063

for molecular states, 1039–1077

of simple model system, 1040–1046

summary for, 1077

Quantum theory, 619, 640–650

atomic nature of matter, 640–641

Bohr’s theory of hydrogen atom, 646–650

Einstein’s theory of photoelectric effect, 645

introduction to, 620

Planck’s theory of blackbody radiation,

641–645

summary for, 652

wave-particle duality of light, 646

Quantum yield, of photochemical reaction,

559, 981

Quasi-equilibrium approximation.See

Equilibrium approximation

Quasi-equilibrium process.SeeReversible

process

Quasi-static process.SeeReversible process

Quasi-steady-state approximation.See

Steady-state approximation

Quenched, reaction, 982–983

R.SeeResistance

Radial distribution function, 751

for dense gases and liquids, 1148

for hydrogen orbitals, 752, 752f

Radial factor

in hydrogen atom wave function, 736–740,

744f, 760

in relative Schrödinger equation, 730

Radiation theory, for unimolecular

reactions, 545

Radiationless transition, 780

Radioactive nuclides, decay of, 490–491

Raman active, 987–988