##### Document Text Contents

Page 2

STANDARD ATOMIC MASSES 1979

(Scaled to the relative atomic mass ,

A ,.(I2C) = 12)

Atomic Atomic Atomic Atomic

Name Symbol number mass Name Symbol number mass

Actinium Ac 89 227.0278 Molybdenum Mo 42 95.94

Aluminium Al 13 26.98154 Neodymium Nd 60 144.24*

Americium Am 95 (243) Neon Ne 10 20. 179

Antimony Sb 51 121.75* Neptunium Np 93 237.0482

Argon Ar 18 39 .948 Nickel Ni 28 58.69

Arsenic As 33 74.9216 Niobium Nb 41 92.9064

Astatine At 85 (210) Nitrogen N 7 14 .0067

Barium Ba 56 137 .33 Nobelium No 102 (259)

Berkelium Bk 97 (247) Osmium Os 76 190.2

Beryllium Be 4 9.01218 Oxygen 0 8 15 .9994*

Bismuth Bi 83 208.9804 Palladium Pd 46 106.42

Boron B 5 10.81 Phosphorus P 15 30.97376

Bromine Br 35 79.904 Platinum Pt 78 195.08*

Cadmium Cd 48 112.41 Plutonium Pu 94 (244)

Caesium Cs 55 132 .9054 Polonium Po 84 (209)

Calcium Ca 20 40 .08 Potassium K 19 39.0983

Californium Cf 98 (25 I) Praseodymium Pr 59 140.9077

Carbon C 6 12.011 Promethium Pm 61 (145)

Cerium Ce 58 140. 12 Protactinium Pa 91 231 .0359

Chlorine Cl 17 35.453 Radium Ra 88 226.0254

Chromium Cr 24 51.996 Radon Rn 86 (222)

Cobalt Co 27 58 .9332 Rhenium Re 75 186.207

Copper Cu 29 63 .546* Rhodium Rh 45 102 .9055

Curium Cm 96 (247) Rubidium Rb 37 85.4678*

Dysprosium Dy 66 162 .50* Ruthenium Ru 44 101.07*

Einsteinium Es 99 (252) Samarium Sm 62 150.36*

Erbium Er 68 167.26* Scandium Sc 21 44.9559

Europium Eu 63 151.96 Selenium Se 34 78 .96*

Fermium Fm 100 (257) Silicon Si 14 28.0855 *

Fluorine F 9 18.998403 Silver Ag 47 107 .868

Francium Fr 87 (223) Sodium Na II 22 .98977

Gadolinium Gd 64 157.25* Strontium Sr 38 87.62

Gallium Ga 31 69.72 Sulfur S 16 32 .06

Germanium Ge 32 72 .59* Tantalum Ta 73 180.9479

Gold Au 79 196.9665 Technetium Tc 43 (98)

Hafnium Hf 72 178.49* Tellurium Te 52 127.60*

Helium He 2 4.00260 Terbium Tb 65 158.9254

Holmium Ho 67 164.9304 Thallium TI 81 204.383

Hydrogen H I 1.0079 Thorium Th 90 232 .0381

Indium In 49 114.82 Thulium Tm 69 168.9342

Iodine I 53 126.9045 Tin Sn 50 118 .69*

Iridium Ir 77 192 .22* Titanium Ti 22 47 .88*

Iron Fe 26 55 .847* Tungsten W 74 183.85*

Krypton Kr 36 83 .80 (U nnilhexium) (Unh) 106 (263)

Lanthanum La 57 138.9055* (Unnilpentium) (Unp) 105 (262)

Lawrencium Lr 103 (260) (U nnilquadium) (Unq) 104 (261)

Lead Pb 82 207.2 Uranium U 92 238.0289

Lithium Li 3 6.941 * Vanadium V 23 50.9415

Lutetium Lu 71 174 .967* Xenon Xe 54 131.29*

Magnesium Mg 12 24.305 Ytterbium Yb 70 173 .04*

Manganese Mn 25 54.9380 Yttrium Y 39 88.9059

Mendelevium Md 101 (258) Zinc Zn 30 65.38

Mercury Hg 80 200.59* Zirconium Zr 40 91.22

Source: Pure and Applied Chemistry , 51, 405 (1979). By permission .

Value s are considered reliable to ± I in the last digit or ± 3 when followed by an asterisk(*). Values in

parentheses are used for radioactive elements whose atomic weights cannot be quoted precisel y without

knowledge of the origin of the elements; the value given is the atomic mass number of the isotope of that

element of longest known half-life.

Page 519

Multiplying /1px by /1x, we obtain

The U ncerta i nty Pr inc ip le 489

Since the radical is greater than unity for all values of n, we have the result,

h /1p · /1x > -x 4n ' (21 .24)

The inequality (2 1 .24) is the statement of the Heisenberg uncertainty principle for the

particle in the box.

21 .4 T H E U N C E RTAI N TY P R I N CI P L E

The situation for the free particle compared with the particle in the box may b e summarized

as follows.

1. The free particle has an exactly defined momentum, but the position is completely

indefinite.

2. When we try to gain information about the position of the particle by confining it

within the length L, an indefiniteness or uncertainty is introduced in the momentum.

The product of these uncertainties is given by the inequality (2 1 .24) /1Px/1x > h/4n.

3. If we attempt to give the particle a precise position by letting L --> 0, then to satisfy

(2 1 .24), /1px --> 00 ; the momentum becomes completely indefinite.

These facts are given general expression by the Heisenberg uncertainty principle,

which we may state in the form : the product of the uncertainty in a coordinate and the

uncertainty in the conjugate momentum is at least as large as h/4n. (By the conjugate

momentum of a coordinate we mean the component of momentum along that coordinate.)

In Cartesian coordinates we can state the uncertainty principle by the relations

h /1p · /1x > -x - 4n '

h /1p . /1y > -Y - 4n '

h /1p · /1z > -Z - 4n ' (21 .25)

In passing, we reiterate that the operators for Px and x do not commute. Variables having

operators that do not commute are subject to uncertainties that are related as in (21 .25). It

follows from this principle that it is not possible to measure exactly and simultaneously

both the x position and the x component of the momentum of a particle. Either the position

or the conjugate momentum may be measured as precisely as we please, but increase in

precision in the knowledge of one results in a loss of precision in the knowledge ofthe other.

Suppose that we attempt a precise measurement of the position of a particle using a

microscope. The resolving power of a microscope is limited by the wavelength of the light

used to illuminate the object ; the shorter the wavelength (the higher the frequency) of the

light used, the more accurately the position of the particle can be defined. If we wish to

measure the position very accurately, then light of very high frequency would be required ;

a y-ray, for example. To be seen, the y-ray must be scattered from the particle into the

objective of the microscope. However, a y-ray of such high frequency has a large momentum ;

if it hits the particle, some of this momentum will be imparted to the particle, which will be

kicked off in an arbitrary direction. The very process of measurement of position introduces

an uncertainty in the momentum of the particle.

Page 520

490 The Quantum M echan ics of Some S imp le Systems

y-ray

E = hv

Py =l1J!

Scattered

E' = hv' ray

P ' E = -2m

, hv' pY =c

F i g u re 21 .3 The Compton effect.

The scattering of a y-ray by a small particle and the accompanying recoil of the particle

is called the Compton effect (Fig. 2 1 . 3). Let p be the momentum of the particle after the

collision ; the momentum of the y-ray is obtained from the energy hv, which according to

the Einstein equation, must be equal to my c2 • Therefore the momentum of the y-ray is

myc = hv/c before the collision and hv'/c after the collision. Energy conservation requires

that

I

p2

hv = hv + 2m '

while momentum conservation requires that for the x component

and for the y component

hv hv'

- = � cos ¢ + P cos e, c c

hv'

o = - sin ¢ - p sin e. c

In addition to the original frequency v, these three equations involve four variables : Vi, p, ¢,

and e. Using two of these equations, we can eliminate e and v', and reduce the third to a

relation between p and ¢. If the particle is to be seen, the y-ray must be scattered into the

objective of the microscope, that is, within a range 11¢. Since 11¢ is finite, there is a cor

responding finite range of values, an uncertainty, in the particle momentum p. The process

of measurement itself perturbs the system so that the momentum becomes indefinite even if

it were not indefinite before the measurement. Since no method of measurement has been

devised that is free from this difficulty, the uncertainty principle is an accepted physical

principle. Examination of the equations for the Compton effect shows that this difficulty is

a practical one only for particles with a mass of the order of that of the electron or of that

of individual atoms. It does not give trouble with golf balls.

Another important uncertainty relation occurs in time-dependent systems. We can

take the result for the particle in a box, which classically is written E = p;/2m ; if the

momentum has an uncertainty I1px , then there is a corresponding uncertainty in the energy,

I1E = (8E/8pJl1px , and thus

I1E = (l/m)px I1px = {l/m) (mvJ I1px = Vx I1px '

However, the velocity, vx , can be written Vx = I1x/l1t ; using this result in the equation for

I1E yields I1E . I1t = I1px . I1x ; extending this argument to the general case we have

h I1E · l1t > �. - 4n (21 .26)

Page 1037

ultracentrifugation, 929

ultracentrifuge , 935ff.

ultraviolet catastrophe , 453

ultraviolet photoelectron spectroscopy, 6 1 8

ultraviolet radiation , 583

uncertainty , definition of, 487 ff.

uncertainty principle , 477 , 489ff.

ungerade, 652

unimolecular reactions , 8 1 4 , 8 1 7

theory of, 852

universe , entropy of, 1 96

uranium

fission, 827

fluorescence of salts of, 450

valence bond method, 532

for hydrogen molecule , 534

valence shell electron pair repulsion, 546

van der Waals bonds , 690

van der Waals constants , 67 1ff.

table of, 36

van der Waals crystal s , 682

van der Waals equation , 47 , 34ff.

isotherms of, 42

van der Waals forces , 85 , 427 , 437 , 659 , 7 12

van der Waals solid , 7 1 3

van't Hoff, 446

van't Hoff equation , 289

vapor pressure , 40 , 88

activities and , 350

effect of pressure on , 270

lowering , 279, 28 1

of binary solution, 297ff.

of polymer solutions, 920ff.

of salt hydrates , 336

of small droplets , 414

vaporization , heat of, 88

vaporization equilibrium, 242

variable

dependent , 1 5 , A- I , A-3

independent , 1 5 , A- I , A-3

of state , definition of, 1 04

variables

composition , 1 8

natural , 209

reduced , 45

separation of, 499

variation theorem, 532

vectors , A-7

velocity components , 6 1

velocity distribution , 57

velocity space , 6 1

velocity vector, component of, 54

vertical transition, 642

vibration-rotation band, 626 , 628ff.

for Hel molecule , 630

P-branch , 629

Q-branch , 633

R-branch , 629

vibrational energy, 74ff.

vibrations , 53 1 , 628

virial equation , 47

viscosimeter, 760

viscosity , 90, 746

coefficient of, 752 , 766, 781

film, 426

intrinsic , 940

of polymer solutions , 9 1 9 , 940

specific , 940

visible radiation , 583

Yolta, A . , 395

voltage efficiency , 398

volume of mixing, 229

von Laue, M. , 700

von Weimarn ' s law, 4 1 6

YSEPR, 546

vulcanization , 9 1 6

Walden' s rule , 782

water

boiling point of, 676

infrared absorption bands , 636

microwave spectrum of, 635

molecular geometry , 543

phase diagram, 266

photoelectron spectrum of, 620

water molecule

electronic configuration for, 646

energy levels for, 574

symmetry properties of, 562

wave functions for, 57 lff.

wave equation , classical , 460ff.

wave function, 463ff.

determinantal , 588 , 593

for electron pair , 533

for hydrogen atom, 5 1 4

for hydrogen molecule , 533ff.

for particle in a box , 48 1

interpretation of, 463

normalized , 464 , 468

nuclear spin , 735

one-electron, 588

symmetry of, 5 34 , 556 , 560

symmetry under interchange , 735

wave mechanics , 460

wave nature of matter, 447

wave number, 627

definition of, 58 1

wavelength

definition of, 58 1

of a particle , 459ff.

of electrons , 447

Werner, A . , 447

wet residues , method of, 342

Wheatstone bridge , 770

Wien effect, 786

Wien' s displacement law , 453

Wilhelmy, 799

Wohler , 446

work

electrical , 206

expansion, 1 06

maximum and minimum, 1 10

thermodynamic , definition of, 104

work function , 205

x-ray diffraction

and hydrogen bonding, 678

in liquids , 705

pattern , symmetry of, 693

x-ray diffractometer, 702

x-ray examination of crystals , 700

x-ray fluorescence spectroscopy , 6 14ff.

x-ray frequencies , 58 1

x-ray microanalysis , 6 1 5

x-ray photoelectron spectroscopy, 6 17

x-ray spectroscopy , 609ff.

x-rays , 446 , 583

absorption of, 622

discovery of, 447

Zeeman effect , 600 , 622

anomalous , 602

normal , 601

Zeroth law (see thermodynamics ) , 96

zeta potential , 435 , 438

Ziegler, K . , 9 1 6

STANDARD ATOMIC MASSES 1979

(Scaled to the relative atomic mass ,

A ,.(I2C) = 12)

Atomic Atomic Atomic Atomic

Name Symbol number mass Name Symbol number mass

Actinium Ac 89 227.0278 Molybdenum Mo 42 95.94

Aluminium Al 13 26.98154 Neodymium Nd 60 144.24*

Americium Am 95 (243) Neon Ne 10 20. 179

Antimony Sb 51 121.75* Neptunium Np 93 237.0482

Argon Ar 18 39 .948 Nickel Ni 28 58.69

Arsenic As 33 74.9216 Niobium Nb 41 92.9064

Astatine At 85 (210) Nitrogen N 7 14 .0067

Barium Ba 56 137 .33 Nobelium No 102 (259)

Berkelium Bk 97 (247) Osmium Os 76 190.2

Beryllium Be 4 9.01218 Oxygen 0 8 15 .9994*

Bismuth Bi 83 208.9804 Palladium Pd 46 106.42

Boron B 5 10.81 Phosphorus P 15 30.97376

Bromine Br 35 79.904 Platinum Pt 78 195.08*

Cadmium Cd 48 112.41 Plutonium Pu 94 (244)

Caesium Cs 55 132 .9054 Polonium Po 84 (209)

Calcium Ca 20 40 .08 Potassium K 19 39.0983

Californium Cf 98 (25 I) Praseodymium Pr 59 140.9077

Carbon C 6 12.011 Promethium Pm 61 (145)

Cerium Ce 58 140. 12 Protactinium Pa 91 231 .0359

Chlorine Cl 17 35.453 Radium Ra 88 226.0254

Chromium Cr 24 51.996 Radon Rn 86 (222)

Cobalt Co 27 58 .9332 Rhenium Re 75 186.207

Copper Cu 29 63 .546* Rhodium Rh 45 102 .9055

Curium Cm 96 (247) Rubidium Rb 37 85.4678*

Dysprosium Dy 66 162 .50* Ruthenium Ru 44 101.07*

Einsteinium Es 99 (252) Samarium Sm 62 150.36*

Erbium Er 68 167.26* Scandium Sc 21 44.9559

Europium Eu 63 151.96 Selenium Se 34 78 .96*

Fermium Fm 100 (257) Silicon Si 14 28.0855 *

Fluorine F 9 18.998403 Silver Ag 47 107 .868

Francium Fr 87 (223) Sodium Na II 22 .98977

Gadolinium Gd 64 157.25* Strontium Sr 38 87.62

Gallium Ga 31 69.72 Sulfur S 16 32 .06

Germanium Ge 32 72 .59* Tantalum Ta 73 180.9479

Gold Au 79 196.9665 Technetium Tc 43 (98)

Hafnium Hf 72 178.49* Tellurium Te 52 127.60*

Helium He 2 4.00260 Terbium Tb 65 158.9254

Holmium Ho 67 164.9304 Thallium TI 81 204.383

Hydrogen H I 1.0079 Thorium Th 90 232 .0381

Indium In 49 114.82 Thulium Tm 69 168.9342

Iodine I 53 126.9045 Tin Sn 50 118 .69*

Iridium Ir 77 192 .22* Titanium Ti 22 47 .88*

Iron Fe 26 55 .847* Tungsten W 74 183.85*

Krypton Kr 36 83 .80 (U nnilhexium) (Unh) 106 (263)

Lanthanum La 57 138.9055* (Unnilpentium) (Unp) 105 (262)

Lawrencium Lr 103 (260) (U nnilquadium) (Unq) 104 (261)

Lead Pb 82 207.2 Uranium U 92 238.0289

Lithium Li 3 6.941 * Vanadium V 23 50.9415

Lutetium Lu 71 174 .967* Xenon Xe 54 131.29*

Magnesium Mg 12 24.305 Ytterbium Yb 70 173 .04*

Manganese Mn 25 54.9380 Yttrium Y 39 88.9059

Mendelevium Md 101 (258) Zinc Zn 30 65.38

Mercury Hg 80 200.59* Zirconium Zr 40 91.22

Source: Pure and Applied Chemistry , 51, 405 (1979). By permission .

Value s are considered reliable to ± I in the last digit or ± 3 when followed by an asterisk(*). Values in

parentheses are used for radioactive elements whose atomic weights cannot be quoted precisel y without

knowledge of the origin of the elements; the value given is the atomic mass number of the isotope of that

element of longest known half-life.

Page 519

Multiplying /1px by /1x, we obtain

The U ncerta i nty Pr inc ip le 489

Since the radical is greater than unity for all values of n, we have the result,

h /1p · /1x > -x 4n ' (21 .24)

The inequality (2 1 .24) is the statement of the Heisenberg uncertainty principle for the

particle in the box.

21 .4 T H E U N C E RTAI N TY P R I N CI P L E

The situation for the free particle compared with the particle in the box may b e summarized

as follows.

1. The free particle has an exactly defined momentum, but the position is completely

indefinite.

2. When we try to gain information about the position of the particle by confining it

within the length L, an indefiniteness or uncertainty is introduced in the momentum.

The product of these uncertainties is given by the inequality (2 1 .24) /1Px/1x > h/4n.

3. If we attempt to give the particle a precise position by letting L --> 0, then to satisfy

(2 1 .24), /1px --> 00 ; the momentum becomes completely indefinite.

These facts are given general expression by the Heisenberg uncertainty principle,

which we may state in the form : the product of the uncertainty in a coordinate and the

uncertainty in the conjugate momentum is at least as large as h/4n. (By the conjugate

momentum of a coordinate we mean the component of momentum along that coordinate.)

In Cartesian coordinates we can state the uncertainty principle by the relations

h /1p · /1x > -x - 4n '

h /1p . /1y > -Y - 4n '

h /1p · /1z > -Z - 4n ' (21 .25)

In passing, we reiterate that the operators for Px and x do not commute. Variables having

operators that do not commute are subject to uncertainties that are related as in (21 .25). It

follows from this principle that it is not possible to measure exactly and simultaneously

both the x position and the x component of the momentum of a particle. Either the position

or the conjugate momentum may be measured as precisely as we please, but increase in

precision in the knowledge of one results in a loss of precision in the knowledge ofthe other.

Suppose that we attempt a precise measurement of the position of a particle using a

microscope. The resolving power of a microscope is limited by the wavelength of the light

used to illuminate the object ; the shorter the wavelength (the higher the frequency) of the

light used, the more accurately the position of the particle can be defined. If we wish to

measure the position very accurately, then light of very high frequency would be required ;

a y-ray, for example. To be seen, the y-ray must be scattered from the particle into the

objective of the microscope. However, a y-ray of such high frequency has a large momentum ;

if it hits the particle, some of this momentum will be imparted to the particle, which will be

kicked off in an arbitrary direction. The very process of measurement of position introduces

an uncertainty in the momentum of the particle.

Page 520

490 The Quantum M echan ics of Some S imp le Systems

y-ray

E = hv

Py =l1J!

Scattered

E' = hv' ray

P ' E = -2m

, hv' pY =c

F i g u re 21 .3 The Compton effect.

The scattering of a y-ray by a small particle and the accompanying recoil of the particle

is called the Compton effect (Fig. 2 1 . 3). Let p be the momentum of the particle after the

collision ; the momentum of the y-ray is obtained from the energy hv, which according to

the Einstein equation, must be equal to my c2 • Therefore the momentum of the y-ray is

myc = hv/c before the collision and hv'/c after the collision. Energy conservation requires

that

I

p2

hv = hv + 2m '

while momentum conservation requires that for the x component

and for the y component

hv hv'

- = � cos ¢ + P cos e, c c

hv'

o = - sin ¢ - p sin e. c

In addition to the original frequency v, these three equations involve four variables : Vi, p, ¢,

and e. Using two of these equations, we can eliminate e and v', and reduce the third to a

relation between p and ¢. If the particle is to be seen, the y-ray must be scattered into the

objective of the microscope, that is, within a range 11¢. Since 11¢ is finite, there is a cor

responding finite range of values, an uncertainty, in the particle momentum p. The process

of measurement itself perturbs the system so that the momentum becomes indefinite even if

it were not indefinite before the measurement. Since no method of measurement has been

devised that is free from this difficulty, the uncertainty principle is an accepted physical

principle. Examination of the equations for the Compton effect shows that this difficulty is

a practical one only for particles with a mass of the order of that of the electron or of that

of individual atoms. It does not give trouble with golf balls.

Another important uncertainty relation occurs in time-dependent systems. We can

take the result for the particle in a box, which classically is written E = p;/2m ; if the

momentum has an uncertainty I1px , then there is a corresponding uncertainty in the energy,

I1E = (8E/8pJl1px , and thus

I1E = (l/m)px I1px = {l/m) (mvJ I1px = Vx I1px '

However, the velocity, vx , can be written Vx = I1x/l1t ; using this result in the equation for

I1E yields I1E . I1t = I1px . I1x ; extending this argument to the general case we have

h I1E · l1t > �. - 4n (21 .26)

Page 1037

ultracentrifugation, 929

ultracentrifuge , 935ff.

ultraviolet catastrophe , 453

ultraviolet photoelectron spectroscopy, 6 1 8

ultraviolet radiation , 583

uncertainty , definition of, 487 ff.

uncertainty principle , 477 , 489ff.

ungerade, 652

unimolecular reactions , 8 1 4 , 8 1 7

theory of, 852

universe , entropy of, 1 96

uranium

fission, 827

fluorescence of salts of, 450

valence bond method, 532

for hydrogen molecule , 534

valence shell electron pair repulsion, 546

van der Waals bonds , 690

van der Waals constants , 67 1ff.

table of, 36

van der Waals crystal s , 682

van der Waals equation , 47 , 34ff.

isotherms of, 42

van der Waals forces , 85 , 427 , 437 , 659 , 7 12

van der Waals solid , 7 1 3

van't Hoff, 446

van't Hoff equation , 289

vapor pressure , 40 , 88

activities and , 350

effect of pressure on , 270

lowering , 279, 28 1

of binary solution, 297ff.

of polymer solutions, 920ff.

of salt hydrates , 336

of small droplets , 414

vaporization , heat of, 88

vaporization equilibrium, 242

variable

dependent , 1 5 , A- I , A-3

independent , 1 5 , A- I , A-3

of state , definition of, 1 04

variables

composition , 1 8

natural , 209

reduced , 45

separation of, 499

variation theorem, 532

vectors , A-7

velocity components , 6 1

velocity distribution , 57

velocity space , 6 1

velocity vector, component of, 54

vertical transition, 642

vibration-rotation band, 626 , 628ff.

for Hel molecule , 630

P-branch , 629

Q-branch , 633

R-branch , 629

vibrational energy, 74ff.

vibrations , 53 1 , 628

virial equation , 47

viscosimeter, 760

viscosity , 90, 746

coefficient of, 752 , 766, 781

film, 426

intrinsic , 940

of polymer solutions , 9 1 9 , 940

specific , 940

visible radiation , 583

Yolta, A . , 395

voltage efficiency , 398

volume of mixing, 229

von Laue, M. , 700

von Weimarn ' s law, 4 1 6

YSEPR, 546

vulcanization , 9 1 6

Walden' s rule , 782

water

boiling point of, 676

infrared absorption bands , 636

microwave spectrum of, 635

molecular geometry , 543

phase diagram, 266

photoelectron spectrum of, 620

water molecule

electronic configuration for, 646

energy levels for, 574

symmetry properties of, 562

wave functions for, 57 lff.

wave equation , classical , 460ff.

wave function, 463ff.

determinantal , 588 , 593

for electron pair , 533

for hydrogen atom, 5 1 4

for hydrogen molecule , 533ff.

for particle in a box , 48 1

interpretation of, 463

normalized , 464 , 468

nuclear spin , 735

one-electron, 588

symmetry of, 5 34 , 556 , 560

symmetry under interchange , 735

wave mechanics , 460

wave nature of matter, 447

wave number, 627

definition of, 58 1

wavelength

definition of, 58 1

of a particle , 459ff.

of electrons , 447

Werner, A . , 447

wet residues , method of, 342

Wheatstone bridge , 770

Wien effect, 786

Wien' s displacement law , 453

Wilhelmy, 799

Wohler , 446

work

electrical , 206

expansion, 1 06

maximum and minimum, 1 10

thermodynamic , definition of, 104

work function , 205

x-ray diffraction

and hydrogen bonding, 678

in liquids , 705

pattern , symmetry of, 693

x-ray diffractometer, 702

x-ray examination of crystals , 700

x-ray fluorescence spectroscopy , 6 14ff.

x-ray frequencies , 58 1

x-ray microanalysis , 6 1 5

x-ray photoelectron spectroscopy, 6 17

x-ray spectroscopy , 609ff.

x-rays , 446 , 583

absorption of, 622

discovery of, 447

Zeeman effect , 600 , 622

anomalous , 602

normal , 601

Zeroth law (see thermodynamics ) , 96

zeta potential , 435 , 438

Ziegler, K . , 9 1 6