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JWST736-Kolasinski
August 25, 2016
9:56
Printer Name:
Trim: 279mm × 216mm
Index
band gap, 71
band structure, 70
conduction band, 70
valence band, 70
basis set, 478
bathochromic shift, 659
bilayer sheet, 61
binding energy, 562
biochemical standard state, 327
black-body radiation, 547
Bloch waves, 70
blue shift, 540, 659
TE
RI
AL
Bohr condition, 545
Bohr frequency condition See Bohr condition, 551
Bohr radius, 455, 577
boiling point, 60, 234, 235, 241
normal, 45, 60
standard, 45, 60
Boltzmann
factor, 93
Boltzmann constant, 104
Boltzmann distribution, 269
bond
chalcogen, 38
halogen, 38
hydrogen, 38
noncovalent, 38
pnicogen, 38
bond dissociation energy, 190
bond order, 585
Born interpretation, 465
Born-Oppenheimer approximation, 571, 603, 639
Bose-Einstein statistics, 99, 708
boson, 98, 508
broadening
homogeneous, 542, 564, 636
bubble, 246
bubble line, 250
buffer, 293
MA
D
TE
GH
RI
Abbe limit, 680
absorbance, 548
naperian, 548
absorption coefficient, 548
action potential, 329
activated complex, 333, 351, 364, 383
activation
enthalpy, 367
entropy, 367
activation barrier, 383
activation energy, 351, 367, 377
activity, 209, 263, 265
absolute, 264
mean ionic, 290
relative, 264
activity coefficient, 209, 263, 324
mean ionic, 290
adiabat, 142
adiabatic, 124
adsorption
activated, 377
dissociative, 380
Langmuir model of dissociative, 380
nonspecific, 305
precursor-mediated, 380
site, 76, 77
specific, 305, 415
adsorption isotherm, 381
affinity, 204
aggregation, 223
amphiphile, 61, 223
amplifier, 671
angular momentum, 501, 503
anharmonicity, 611, 655, 661
constant, 611
anode, 301
anti-Stokes shift, 659
antisymmetrization, 528, 529, 582
area
specific, 84
Arrhenius plot, 351
atomic unit of time, 577
atomic units, 577
Aufbau principle, 526, 580, 585
Auger electron spectroscopy, 562, 564
autocatalysis, 347, 371
azeotrope, 251
CO
PY
JWST736-IND
calorimetry, 184
capillarity, 244
capillary condensation, 245
capillary force, 245
capillary waves, 61
carbon nanotubes, 82
Carnot cycle, 142
catalysis
acid-base, 402
heterogeneous, 393
homogeneous, 402, 403
catalyst, 333
cathode, 301
cavity ring-down spectroscopy, 683
cell notation, 310
cell potential, 310, 312, 416
standard, 310
cell reaction, 312
central field model, 525
centrifugal distortion, 607
Chain reactions, 407
character, 647
character table, 647
chemical potential, 55, 101, 201, 232, 234, 259, 260, 269,
318
ideal gas, 201
ideal solution, 263
ions in solution, 290
mean ionic, 290
real gas, 264
solute, 263
solvent, 263
Physical Chemistry: How Chemistry Works, First Edition. Kurt W. Kolasinski.
© 2017 John Wiley & Sons, Ltd. Published 2017 by John Wiley & Sons, Ltd.
Companion Website: www.wiley.com/go/kolasinski/physicalchemistry
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Index
chemical shift, 562, 563
chemisorption, 398
classical nucleation theory, 246
Clebsch-Gordon series, 555
cluster, 78
coefficient of performance, 147
coexistence curve, 235, 237
coherent control, 688
colligative property, 273
collision
cross section, 27
density, 28
diameter, 27
frequency, 28
relative mean speed, 28
collision cross section, 362
collision density, 361, 362
color center, 695
combination mode, 649
combination principle, 453
common ion effect, 217
commutator, 469, 481
complementary observables, 481
concentration, 54
amount, 54
conductance, 295
conductivity, 295
molar, 295
configuration interaction, 583
configuration mixing, 535
conformational selection mechanism, 404
conjugate phase, 229
constant
cryoscopic, 274
ebullioscopic, 273
contact angle, 244, 245
coordination number, 50, 51, 76
core electron, 585
core hole lifetime, 564
correspondence principle, 444, 463, 495
corresponding states, 42
Coster-Kronig transitions, 565
Coulomb potential, 515
coupling scheme
jj-coupling, 559
LS coupling, 554
Russell-Saunders, 554
covalent bond, 571
dative, 571
three-center, 571
two-center, 571
coverage, 375, 379
absolute, 394
fractional, 394
critical micelle concentration, 61, 223
critical nucleus size, 246
critical opalescence, 43
critical point, 234, 235
critical point drying, 237
critical separation, 363
crystal modifications, 235
crystallization, 252
current density, 304, 416
diffusion, 60
exchange, 416, 417
migration, 60
degeneracy, 95, 517
degree of dissociation, 215, 295
degree of polymerization, 409
degree of rate control, 354
degrees of freedom, 18
internal, 18
delocalization energy, 597
denaturation, 404
density functional theory, 597
density of states, 96, 102, 707
deposition, 68
desorption, 375
detailed balance, 353
dew line, 250
Dexter electron transfer, 661
diffraction, 694
diffusion, 55
Case II, 57
non-Fickian, 57
diffusion coefficient, 55
dilute gas limit, 96
dipole moment
bond, 651
electric, 650
dipole scattering, 628
Dirac notation, 480
dispersion, 79
dispersion interactions, 37
dissociation energy, 611
distribution
Boltzmann, 91
Bose-Einstein, 100
Fermi-Dirac, 99
Maxwell-Boltzmann, 97, 102
doping, 71
Doppler shift, 542
drift speed, 55
Einstein coefficient
A, 546, 636
B, 546, 635
electric dipole moment, 545
electric double layer, 415
electrical double layer, 305
electrochemical cell, 310
electrochemical potential, 309, 318
electrochemical series, 314, 319
electrode, 310
reference, 310, 317
saturated calomel, 317
silver-silver chloride, 317
standard hydrogen, 310, 314
electrolyte
strong, 295
weak, 295
electromagnetism, 33
electromotive force, 312
emf, 312
electron configuration, 526, 533
electron correlation, 525
electron energy loss spectroscopy, 628
electron number, 302
electron transfer, 326
heterogeneous, 424
inner sphere, 419
Marcus theory, 421
outer sphere, 420
electrons
equivalent, 521
electrophoretic effect, 290
electrostatic interactions, 34
emergent behavior, 88
energy
bond dissociation, 190
Coulomb, 35
electrostatic, 34
equipartition, 25
exchange, 37
Fermi See Fermi energy, 447
Gibbs, 153
Helmholtz, 153
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Index
induction, 36
internal, 25, 52, 89, 112
ionization, 521
kinetic, 21
mean kinetic, 24
vacuum, 447
energy density of radiation, 546, 636
enthalpy, 130
atomization, 191
bond dissociation, 190
combustion, 185, 194
formation, 192
hydration, 191, 268, 287
mixing, 253
mixing, polymer, 278
reaction, 193, 324
solution, 191
solvation, 287
standard change, 182
temperature dependence, 168
transfer, 287
entropy, 140
calorimetric, 172
reaction, 324
residual, 93
spectroscopic, 173
statistical mechanical definition, 92
entropy change
reaction, 173
thermodynamic definition, 148
enzyme, 403
equation
Boltzmann formula, 149
de Broglie, 474
Einstein, 562
Frenkel, 377
Planck radiation formula, 709
angular, 504
Antoine, 242
Arrhenius, 351, 362
Balmer-Rydberg-Ritz formula, 453
Beer-Lambert law, 411, 548
boiling point elevation, 273
Boltzmann formula, 92
Bragg, 442
Butler-Volmer, 417
central equation of thermodynamics, 103
Clapeyron, 239
Clausius inequality, 157
Clausius-Clapeyron, 240, 242
cut off law, 689
Davies, 291
de Broglie relation, 451
Debye-Hückel limiting law, 290
Debye-Hückel-Onsager, 295
Dirac, 507
Einstein, 447
Einstein relation, 55
Einstein-Smoluchowski, 57
Eyring, 367
Faraday’s law, 304
Fermi’s golden rule, 546, 636
freezing point depression, 274
fundamental, 153, 161, 232, 238, 259 See fundamental
equation
Gibbs phase rule, 238
Gibbs-Duhem, 260
Gibbs-Helmholtz, 166
Goldman, 328
grating, 442
Henderson-Hasselbalch, 293
Henry’s Law, 264, 266
Hertz-Knudsen, 378
Hildebrandt-Scatchard, 278
Huddleston, 53
ideal gas law, 104
Kelvin, 243
Kirchhoff’s law, 168
Kohlrausch’s law, 295
Lineweaver-Burk, 407
Mark-Houwink-Sakurada, 59
Maxwell’s relations, 153
Michaelis-Menten, 406
Nernst, 313
Nernst-Einstein, 55
Nernst-Planck, 59, 416
Ostwald’s dilution law, 295
Planck, 445, 446, 540
Polanyi-Wigner, 376
radial, 516
Raoult’s Law, 264, 266
Redlich-Kwong, 42
Rodrigues formula, 499
Rydberg formula, 551
Sackur-Tetrode, 105
Schrödinger, 467
Schrödinger, time-dependent, 468
Schrödinger, time-independent, 468
secular, 592
Shomate, 127, 151, 168
Stirling’s theorem, 91
Stokes-Einstein, 55
Tafel, 416
Tait, 53
Unsöld’s theorem, 556
van’t Hoff, 205, 206
van’t Hoff isochore, 205
equation of state, 16
equilibrium, 162
acid dissociation constant, 214
acid-base, 292
statistical mechanical definition, 92
water ionization constant, 212
equilibrium constant, 324
concentration, 209
pressure, 209
thermodynamic, 209
eutectic, 255
evaporation, 376
excess functions, 273
exciplex, 362
excited states, 18
exciton, 494
excluded volume, 276
expansion coefficient, 68, 133, 229
expectation value, 475
explosions, 410
exposure, 378, 379
extent of reaction, 181
external potential, 318
Förster resonance energy transfer, 661
faradaic process, 304
Faraday constant, 303
Faraday’s law, 304
feedback, 371
femtochemistry, 686
Fermi energy, 70, 306, 319, 446
Fermi resonance, 655, 661
Fermi’s golden rule, 546, 636
Fermi-Dirac
statistics, 99
fermion, 98, 508
Feshbach resonance, 628
fine structure, 554
Flory 𝜃-temperature, 276
Flory-Huggins theory, 253
fluorescence, 626, 659, 677
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Index
fluorescence excitation spectroscopy, 637
fluorescence lifetime, 627, 663
flux, 55
photon, 411
force constant, 611
formation constant, 220
fractional dissociation, 207
Franck-Condon factor, 617, 639
Franck-Condon principle, 617, 639
free particle, 471
free radicals, 407
freezing point
standard, 45
frequency doubling, 674
FRET, 661
frictional coefficient, 55
frontier orbitals, 306, 400
fugacity, 264
fugacity coefficient, 264
fullerenes, 83
fundamental equation, 153, 275
Galvani potential, 318
gas constant, 17
Gaussian type orbitals, 576
generalized gradient approximation, 598
Gibbs energy, 162, 232, 324
activation, 247, 367
formation in solution, 288
ideal gas, 167
mixing, 253
partial molar, 260
reaction, 163, 203
Gibbs phase rule, 238
Gibbs postulate, 89
Gibbs-Thompson effect, 243
glass, 78
glass transition, 252
good quantum number, 502
Gouy layer, 305
Graphene, 82
Gravitation, 33
gravity, 33
green fluorescent protein, 681
Grotrian diagram, 551
Grotthuss-Draper law, 411
ground state, 18
group velocity, 440
gyromagnetic ratio, 508
Hönl-London factor, 639
Hückel approximation, 593
Haber-Bosch process, 401
half-life, 347
half-reaction, 302
Hamiltonian operator, 468
hardness, 221
harmonic generation, 674
harmonic oscillator, 499, 609
harpooning, 362
Hartree, 577
heat, 124
heat capacity, 126
constant pressure, 130
constant volume, 96, 129
ions in solution, 289
temperature dependence, 127
heat engine efficiency, 145
Helmholtz energy, 111, 162
Helmholtz layer, 305, 318
Henry’s law constant, 268
Hermite polynomials, 499
Hermitian, 470
Hermitian matrix, 532
Hermitian operators, 477
Hess’s law, 192
high harmonic generation, 689
high-field physics, 688
Hildebrand’s rule, 230
Hohenberg-Kohn existence theorem, 597
hole, 453
hot band, 654
Hund’s rule
maximum multiplicity, 526
Hund’s rules, 558
hydrogel, 57
hydrogen atom
energy levels, 517
hydrogen atom transfer, 326
hyperfine splitting, 543
hypsochromic shift, 659
ideal gas constant, 104
ideal gas law, 16, 104
ideal solution, 263
solvent vapor pressure, 265
impact parameter, 363
impact scattering, 628
impingement rate, 378
induced fit mechanism, 404
Induction interactions, 36
infinite square well, 490
inhibition, 347, 355
inhibitor, 334, 407
inner potential, 318
interaction parameter
polymer-solvent, 253
interface, 60
interference, 694
intermediate, 333, 368
internal conversion, 623, 662
internal energy, 119
intersystem crossing, 623, 662
intramolecular vibrational redistribution, 661
intrinsic peak width, 564
intrinsic width, 483
inverted region, 423
ionic atmosphere, 290
Ionic liquids, 64
ionic strength, 290
ionization energy, 457
ionization potential, 521
irradiance, 411
irreversible process, 120
isotherm, 142
isothermal compressibility, 133
IVR, 661
Jablonski diagram, 660
junction potential, 312
Kelvin equation, 244
kinetic chain length, 409
kinetic hypothesis, 21
kinetics
differential method, 347
isolation, 343, 347
Langmuirian adsorption, 378
method of initial rates, 347
method of integration, 339, 346
pseudo-order, 342
reversible reaction, 348
Koopmans’ theorem, 521, 534, 562, 587
Kronecker delta function, 477
Lagrange multipliers, 91
Lamb shift, 519
Langmuir, 378
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August 25, 2016
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Index
Langmuir isotherm, 381
Langmuir layer, 61
Laplacian operator, 483
Larmor frequency, 509
laser induced fluorescence, 678, 686
latent heat, 230
lateral interactions, 376
law
Kirchhoff, 184
law of photochemical equivalence, 411
law of thermodynamics
first, 119, 153
second, 119, 141, 148, 153
third, 119, 171
zeroth, 25, 119
LCAO-MO theory, 576
Legendrian operator, 484
Lennard-Jones diagram, 366
level symbol, 558
lifetime, 340, 347, 542
lifetime broadening, 609
Lindemann-Christiansen mechanism, 373
lineshape, 541
Fano, 542
Gaussian, 542
Lorentzian, 541, 636
Voight, 542
lipids, 84
liposome, 61
liquid crystal, 62
macrocycles, 84
macromolecules, 84
macrostate, 89
mass-energy equilvalence, 443
matrix element, 532
Maxwell speed distribution, 23
mean speed, 24
most probable speed, 23
Maxwell’s relations, 153
mean free path, 28, 55, 57
mechanism, 354, 368
composite, 7
Eigen-Wilkins, 387, 429
Eigen-Winkler, 387, 429
Eley-Rideal, 396
hot precursor, 396
Langmuir-Hinshelwood, 394
melting point, 234, 235, 252
standard, 45
membrane potential, 328
meniscus, 244
method of undetermined multipliers, 91
micelle, 61
Michaelis-Menten kinetics, 405
microscopic reversibility, 353
microstates, 89
total number, 90
mixture, 53
mobility, 60
molality, 54
mean ionic, 290
molar mass, 276
number-average, 85, 276
weight-average, 85
molarity, 54
mole fraction, 27
molecular beam, 125
molecular orbital theory, 576
molecular virial theorem, 583
molecularity, 7, 336
moment of inertia, 106, 503, 605, 656
momentum
linear, 21
Mulliken label, 647
multiphoton photoelectron spectroscopy, 682
multipole expansion, 34
nanoparticle, 78
natural lifetime, 662
natural linewidth, 542
natural variables, 161
near-field scanning optical microscope, 680
Nernst equation, 319
Nernst heat theorem, 171
node, 522
non-radiative relaxation, 622
nonelectrolyte, 295
nonlinear effect, 673
nonlinear spectroscopy, 675
nonlinear susceptibility, 673
normal modes, 653
normal transition temperature, 188
normalization, 466, 477, 491
nuclear hyperfine splitting, 519
nuclear magnetic resonance, 510
nuclear spin, 510
nucleation, 246, 248
critical radius, 247
heterogeneous, 249
homogeneous, 249
nucleation center, 249
occupation number, 89
opalescence, 694
open-circuit potential, 306
operator, 469
optical path difference, 440
orbitals
equivalent, 521
order
group, 646
orthogonality, 477, 491
orthonormality, 477
oscillator, 671
harmonic, 476
osmometry, 276
Osmosis, 275
osmotic coefficient, 276
osmotic pressure, 276
overlap density, 578
overlap integral, 578
overpotential, 307
overtone, 649
overvoltage, 416
oxidant, 302
oxidizing agent, 302
pair correlation function, 50
partial differentials, 152
particle in a box, 96, 490, 706
particle on a ring, 503
particle on a sphere, 504
partition function, 93, 104
translation, 102
Pascal’s law, 21
path function, 120
Pauli exclusion principle, 70, 508, 529
Pauli repulsion, 37, 400, 526, 530
perfect gas, 21
periodic table, 526
perturbation, 654, 655
perturbations, 535
phase diagram
𝜇-T, 233
liquid-vapor, 250
pressure-temperature, 235
phase stability, 233
723
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Index
phase transition, 188, 229
first-order, 230
second-order, 230
standard enthalpy, 188
phase velocity, 435
phosphorescence, 659
photoactivated localization microscopy, 681
photochemical reactions, 411
photochemistry, 686
photodissociation, 413, 624, 686
photoelectric effect, 446
photoemission, 446, 561 See photoelectric effect
photon flow, 411
photosynthesis, 691
physisorption, 398
Planck distribution, 446
Planck quantization hypothesis, 445
plasmon, 694
plot
van’t Hoff, 205, 213
point group, 646
poison, 401
Polanyi rules, 382
polarizability, 36
polydispersity index, 409
polymerization
chain, 408
step, 409
polymers, 84, 252, 277
ponderomotive energy, 690
population, 89, 149
population inversion, 669
porosity, 84
porous solid, 83
postulates of quantum mechanics, 463
potential
(exp-6), 49
Born-Mayer, 37
Lennard-Jones, 42, 48
Morse, 611
potential of zero charge, 305
pre-exponential factor, 351
precipitation, 218
predissociation, 624
pressure, 21
partial, 27
principle
Le Châtelier’s, 204
maximum hardness, 221
product, 333
promoter, 401
proton transfer, 326
proton-coupled electron transfer, 326, 404
pulse shaping, 688
pump-probe experiment, 675, 686
Q switching, 672
quantity calculus, 7
quantum confinement, 494
quantum defect, 535
quantum dot, 495
quantum particles
composite, 452
elementary, 452
quantum yield, 413, 622, 626, 662
quenching, 413, 626, 662
radial distribution function, 50, 286
radial wavefunction, 516
Raman
stimulated scattering, 679
Raman effect, 614
Raman shift, 616
rate
net reaction, 349
rate constant, 336
effective, 339
true, 339
rate determining step, 337, 354
rate law, 333
reactant, 333
reaction
partial order, 336
elementary, 7, 336
mechanism, 7, 369
net, 7
order, 336
rate, 335
standard combustion, 186
reaction chart, 6
reaction isotherm, 203
reaction quotient, 203
real solution
chemical potential, 263
real solutions, 258
real states, 614
red shift, 540, 659
redox couple, 302
reducing agent, 302
reductant, 302
reorganization energy, 422
representation
irreducible, 647
reducible, 649
resonance energy, 597
resonance enhanced multiphoton ionization, 681
resonance scattering, 628
rest potential, 306
reversible process, 120
rigid rotor, 503, 604
ripening
Ostwald, 243
Smoluchowski, 243
Ritz combination principle, 541
rotational angular momentum, 605
rotational branches, 611, 654
rotational constant, 19, 605
rotational energy, 605
rotational term, 605
polyatomic, 656
RRKM theory, 374
Rydberg, 519
Rydberg constant, 517, 551
Rydberg series, 535
Sabatier principle, 399
salt effect, 294
SATP, 3
saturation, 670
saturation ratio, 247
scanning tunneling microscopy, 495
Schemochromes, 698
Schottky anomaly, 111
screening, 33, 586, 587
selection rule
rotation, 655
vibration, 649, 653
selection rules, 620, 638
multiphoton, 675
self-assembly, 222
selvage, 77
Shannon radius, 286
shape resonance, 628
shell, 521, 522
shielding, 510
site blocking, 378
JWST736-IND
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Index
Slater type orbitals, 576
solubility
gas, 268
solubility constant, 268
solubility parameter, 278
Hildebrand, 278
solubility product, 217, 293
solute, 53
solution, 53
electrolyte, 53
ideal-dilute, 272
miscible, 54
nonelectrolyte, 53
regular, 272, 273
solvation number, 285
solvation shell, 284
solvent, 53
Solvophilicity, 280
space quantization, 507, 509
spectator, 333
spectroscopy
two-dimensional, 544
spherical harmonics, 505, 516
spin, 507, 529, 618
spin flip, 508
spin multiplicity, 528, 657
spin-orbit coupling, 518, 552, 554, 619, 639, 657
Spontaneous emission, 546, 636
spontaneous emission, 622
stability constant, 220
standard ambient temperature and pressure, 3, 45
standard formation reaction, 164
standard state, 182, 258, 263
biochemical, 210
electrochemical, 309
physical chemistry, 210
standard temperature and pressure, 3
standard transition temperature, 188
Stark effect, 543, 606
State designations
polyatomic, 656
state function, 120
stationary state, 468
steady-state approximation, 371
steric factor, 362
Stern layer, 305
Stern-Gerlach experiment, 509
Stern-Gouy model, 318
Stern-Volmer constant, 627
Stern-Volmer plot, 627, 663
sticking coefficient, 378
stimulated chemistry, 4
stimulated emission, 546, 669
stimulated emission depletion microscopy, 680
stimulated emission pumping, 679
stoichiometric coefficient, 5, 163, 181
stoichiometric number, 5, 163, 181
Stoichiometric numbers, 335
Stokes shift, 659
STP, 3
strong force, 33
sublimation, 68, 234, 242
subshell, 521
sum frequency generation, 674
supercooling, 247
supercritical CO2 , 279
supercritical fluid, 235
superheating, 247
supersaturation, 247, 249
surface, 60
exterior, 84
interior, 84
surface energy, 246
surface lifetime, 377
surface potential, 318
surface tension, 122, 242, 246
swelling coefficient, 277
symmetry, 574
𝜋, 579
𝜎, 578
element, 643
operation, 643
term symbol, 556, 558, 618
theorem
Carnot, 145
thermal chemistry, 4
thermal wavelength, 102
thermodynamic limit, 16, 78
total angular momentum, 554, 557, 619, 657
transfer coefficient, 417
transference number, 60
transform-limited pulsewidth, 685
transition
bound-bound, 520
bound-free, 521
congruent, 229
non-radiative, 622, 661
transition dipole moment, 546, 549, 550, 617,
639
transition rate, 545, 635
transition state, 364, 365, 377, 383, 422, 687
transition state theory, 366
transmission coefficient, 367
transmittance, 548
triple point, 26, 235, 237
Trouton’s rule, 230
tunneling, 495
decay constant, 497
decay length, 497
transmission coefficient, 497
turnover number, 406
Tyndall scattering, 694
ultraviolet catastrophe, 445
uncertainty principle, 481
universal gas constant See gas constant, 17
vacuum energy, 71
valence bond theory, 573
valence electron, 585
van der Waals forces, 37
vapor pressure, 60, 234, 240, 242, 250, 265
saturation, 265
solute, 266
vaporization, 241
variable
conjugate, 123
extensive, 123
intensive, 123
variational principle, 479, 579, 591
vertical transition, 617, 639
vibration-rotation interaction constant, 607
vibrational overlap, 617, 639
vibrational relaxation, 661
vibrational term, 609
polyatomic, 655
viral expansion
osmotic pressure, 276
virial coefficient, 39
virial expansion, 39
virtual states, 614, 675
viscosity, 56, 57
coefficient, 58
vision, 696
vitrification, 252
725
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9:56
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Trim: 279mm × 216mm
Index
Volta potential, 318
volume
partial molar, 258
water ionization constant, 212
wavefront, 440
wavefunction
spacetime, 465
spatial, 465
wavepacket, 474, 686, 688
weak force, 33
work, 121
work function, 71, 319, 446, 447
X-ray photoelectron spectroscopy, 562
Zeeman effect, 543, 555
zero point energy, 365, 500, 611
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