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Titlecastellan physical chemistry
TagsChemistry
LanguageEnglish
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Total Pages1038
Table of Contents
                            Cover
Title Page
Contents
1 Some Fundamental Chemical Concepts
2 Empirical Properties of Gases
                        
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

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