Modern Physics from [alpha] to Z⁰ [1 ed.] 0471572705

Table of contents :
Cover
Data
PREFACE
CONTENTS
1. SURVEY OF
PARTICLES AND
FORCES
2. DISTRIBUTION
FUNCTIONS
AND kT
3. PLANCK ’S CONSTANT
4. SPECIAL
RELATIVITY
5. WAVE PROPERTIES OF
PARTICLES AND THE
UNCERTAINTY PRINCIPLE
6. RUTHERFORD
SCATTERING
7. THR SCRÖDINGER EQUATION
8. THE HYDROGEN ATOM
9. BEYOND TH E
HYDROGEN
ATOM
10. MOLECULES AND MOLECULAR SPECTRA
11. THE
NUCLEUS
12. QUANTUM STATISTICS
13. MASERS AND LASERS
14. CONDUCTORS, INSULATORS, AND SEMICONDUCTORS
15. SUPERCONDUCTIVITY
16. HIGH-ENERGY PHYSICS: THE GADGETS
17. HIGH-ENERCY PHYSICS:
CLASSIFICATION
OF THE PARTICLES
18. HIGH-ENERGY PHYSICS: UNIFICATION OF THE FORCES
19. THE EARLY UNIVERSE
Colour Supplement
Appendices
A: PHYSICAL
CONSTANTS
B: MAXWELL’S
EQUATIONS
C: VECTOR
CALCULUS
D: DISTRIBUTION
FUNCTIONS
E: SPHERICAL
COORDINATES
F: THE
TAYLOR
EXPANSION
G: TRANSFORMATION
OF ELECTRIC AND
MAGNETIC FIELDS
H: THE
HYDROGEN
ATOM
I: FAMOUS
EXPERIMENTS
IN MODERN PHYSICS
J: OUTSTANDING
PROBLEMS
K: NUCLEAR
DATA
L: TABLE OF
PARTICLE
PROPERTIES
ANSWERS TO SELECTED PROBLEMS
EXAMPLE
INDEX
INDEX
Data

Citation preview

JO H N WILEY & SONS, IN C New York ®Chichester ®Brisbane Toronto « Singapore

N a = 6.02 X-1023

h = 6.63 x 10~34 J s = 4.14 x lO " 15eV-s

c = 3.00 x 108 m/s

h = 1.06 x 10-34 J s = 6.58 x lO’16 eV s

e = 1.60 x 10-|9 C

G = 6.67 x 10"" m3 kg_1-s~2

k = 8.62 x 10"5 eV/K

GP = 8 .9 6 x 10-8 GeV fm3

U s e fu l C o m b in a tio n s

ke2 = 1.44 eV-nm

k T = 0.02585 eV at 7 = 300 K

he = 1240 eV-nm

h c = 197 eV-nm

a = ke2 _ 1

j a 2m c 2 = 13.6 eV

he

a 0 =-

137

he = 0.0529 nm amc1

Ac =

= 2.43 pm me2

eh /in = ^ — = 5 .7 9 x l0 -5 eV T

o =

2m

n^k*

15h 3c 2

= 5 .6 7 x 10-8 W- m~2-K -4

M a s te r E q u a tio n s

Energy and tem perature

(E k ) = ~kT

M axw ell-B oltzm ann distribution

/ MB = C e ~ ElkT

Therm al radiation (pow er per area per unit wavelength)

Energy, m ass, and m om entum

W avelength and m om entum

Schrodinger equation

E = ]j ( m e 2 j + ( p c )

X=— P

- - — V 2y/ + V\f/ = E y

— = ------2 ttAc^____ dX X5 ( e h ci m - i )

E n e r g y u n its Energy

Physical Interpretation

eV

E n erg y scale o f th e outer elec tro n s in atom s

k eV = 103 eV

E n erg y scale o f th e inner electro n s in h eav y atom s

M eV = 106 eV

E n erg y scale o f n eu tro n s and p ro to n s in sid e n u clei

G eV = 109 eV

E n erg y scale o f quarks in sid e pro to n s

T e V = 1 0 12 eV

E n erg y scale to be stu d ied by the n ex t g en e ratio n o f p article p h y sics ex p erim en ts

C o n v e rs io n s f

’

1 eV = 1.60 x 10- 19 J 1 u = 1.66 x 10-27 kg = 931.5 M eV /c2

M ass E n e r g ie s

electron

0.511 M eV

alph a

3730 M eV

p ro to n

938 M eV

W

80 G eV

n eu tron

940 M eV

Z°

91.2 G eV

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CO

MODERN PHYSICS from

CL

to Z°

James William Rohlf Professor o f Physics Boston University

John Wiley & Sons,Inc. New York Chichester Brisbane Toronto Singapore

C h ap ters 1, 2, 3, 4, 5, 6, 7, 9, 11, and 14 C ourtesy A m erican In stitu te o f P hysics. C h ap ter 8 C o u rtesy U rsu la Lam b. C h ap ter 10 C ou rtesy U niversity o f W isco n sin -M ad iso n A rchives. C h ap ter 12 C ou rtesy C avendish L aboratory. C h ap ters 13 and 15 C o urtesy A T & T B ell L aboratories. C h ap ter 16 C ou rtesy C ornell U niversity A rchives, P hoto by S ol G oldberg. C h ap ter 17 C ou rtesy M urray G ell-M an n . C h ap ter 18 C ou rtesy S tev en W einberg. C h ap ter 19 C ou rtesy C alifornia In stitu te o f T echnology.

A C Q U IS IT IO N S E D IT O R M A R K E TIN G M A N A G ER S E N IO R P R O D U C T IO N E D IT O R D E SIG N E R M A N U FA C T U R IN G M A N A G ER P H O T O R E SEA R C H E R IL L U S T R A T IO N C O O R D IN A T O R D IG IT A L PR O D U C TIO N

C liff M ills C atherine F aduska K atharine Rubin K evin M urphy A ndrea Price H ilary N ew m an Jaim e Perea Jen n ifer D ow ling

T h is b o o k w as se t in T im es R om an by D igital P roduction an d printed and b o u n d b y H am ilton P rin tin g C om pany. T he cover w as prin ted b y H am ilton P rin tin g C om pany.

R ecognizing the im portance o f p reserv in g w hat has b een w ritten, it is a p o licy o f Jo h n W iley & S ons, Inc. to h ave b o oks o f en d u rin g value published in the U n ited States on acid-free paper, and w e exert o u r best e ffo rts to th a t end.

C o p yrig h t © 1994, by John W iley & S ons, Inc. All rig h ts reserv ed . P u b lished sim ultaneously in C anada. R ep ro d u ctio n o r tran slation o f any part o f this w o rk beyond th at p erm itted b y S ections 107 a n d 108 o f th e 1976 U nited S tates C opyright A ct w ith o u t the p erm ission o f th e copyright o w n er is u nlaw ful. R eq uests fo r perm ission o r fu rth er in form ation sh o u ld b e ad dressed to the P erm issio n s D epartm ent, John W iley & S ons, Inc. L ib ra r y o f C o n g ress C a ta lo g in g in P u b lic a tio n D ata: R ohlf, Jam es W illiam . M odern p h y sics from [alpha] to Z° / Jam es W illiam R ohlf. — 1st ed. p. cm . In clu d es index. ISB N 0 -471-57270-5 (cloth) 1. P hysics. I. Title. Q C 2 1 .2 .R 6 2 1994 5 3 9 —d c2 0 93-48737 C IP P rinted in th e U nited S tates o f A m erica 109 8 7 6 5 4 3 2

To Tanya chi non risica, non rosica

PREFACE

M o d ern P h ysics fr o m a to Z° is w ritten for an introductory co u rse in m odem physics taken by physics m ajors and en g in eerin g students, usually during th e second year. The p rim ary goal o f th e book is to explain th e observed basic p ro p erties o f atom s. T he prerequisites are calculus-based introductory m echanics and electrom agnetism . T h e intention is to bring th e student to th e exciting frontiers o f p h ysics in a sim ple, com prehensible m anner, w h ile a t th e sam e tim e providing enough detail to satisfy th e intellectual curiosity o f a hungry student. T h is ap­ p ro ach has an advantage fo r the student w ho w ill have a ready reference fo r an introduction to m a n y advanced concepts. It is an advantage fo r the p ro fesso r w ho has the flexibility to choose th e p a c e an d content o f th e course. In this sen se I believe that “ m o re is better.” T h e tex t b eg in s w ith an in tro d u ctio n to p articles and fo rces, in o rd er to m a k e a con n ectio n w ith b asic m e ch an ­ ics an d elec tro m ag n e tism , as w ell as to g iv e a broad o v erv iew o f p h y sics. T h e m o st im p o rta n t p a rt o f special re la tiv ity n ee d ed fo r th e re st o f th e course, m ass and b in d in g en erg y , is in tro d u ced in C h ap ter 1. D istribution fu n ctio n s are in tro d u ced in C h a p te r 2. T h e tim e spent h ere w ill p a y d iv id e n d s w h en p article w a v e fu n ctio n s are d isc u sse d in the c o n tex t o f th e S ch ro d in g er equatio n . It is also im p ossible to grasp th e sig n ifican ce o f energy q u an tiza tio n , d isc o v ered b y P lanck (C h ap ter 3), w ithout firs t u n d ersta n d in g th e M ax w ell-B o ltzm an n d istrib u ­ tion. S p ecial rela tiv ity (C h ap ter 4 ) is in c lu d ed a fte r a d isc u ssio n o f th e p h o to electric effect, w h en it is n ee d ed

to ex p lain th e resu lts o f sc atterin g ex p erim en ts (e.g ., C o m p to n scatterin g ). T h e tex t is d iv id ed into th ree parts. C hapters 1-9 co m p rise th e core. C h ap ter 10 is a short d iscussion o f m o lecu les an d C h ap ter 11 covers th e b asics o f n uclear physics. C hapters 12-15 are an introduction to condensed m atter p h y sics and C hapters 1 6 -1 9 are an introduction to particle p h y sics an d cosm ology. M y experience in teach ­ in g a one sem ester course is th at th e core m aterial in C hapters 1 -9 ca n b e covered in 1 0 -1 2 w eeks. T h e rem ain ­ ing tim e can b e u sed to co v er p arts o f C hapters 10 and 11 and then concentrate on eith er to p ics in co n d en sed m atter p h y sics o r to p ics in p article physics. T h e instructor that w ish es to go m o re slow ly m ay ch o o se to sp en d th e entire sem ester on th e core m aterial and p erh ap s assig n other chapters as optional reading. T h e m ore am bitious in stru c­ to r m ay w ell ch o o se to cover th e core m o re rapidly, d epending on th e background o f th e students. M aterial ap p earin g b etw een asterisk s is m arked “ chal­ lenging.” T h ese sections co ntain p ertin en t m aterial th at is n ot o rd in arily cov ered in th e first m o d ern physics course. M uch o f th is m aterial m ay b e om itted on th e first reading, i f desired, w ith o u t lo ss o f continuity. T h e list o f references an d suggestions fo r fu rth er read in g at th e en d o f each ch ap ter are intended to serve as a starting p o in t for those w ish in g to delve d eep er in to a subject. T h e questions and p ro b lem s are an im portant p art o f th e book. T h ese v ary in d eg ree o f d ifficu lty w ith th e m o st ch allen g in g denoted w ith an asterisk. v

I h av e received m uch sou n d advice from the follow ing p erso n s w ho patien tly read early drafts o f th is book: P ro fesso r G ordon J. A ubrecht (O hio State U niv.), P ro fessor B ernard C hasan (B oston U niv.), P ro fessor H arris K agan (O hio S tate U niv.), and P ro fessor John W . N orthrip (S outhw est M issouri S tate U niv.). In ad dition, th e follow ing p ersons have m ade valuable suggestions on one o r m ore chapters: P rofessors Steve A hlen (B oston U niv.), E d B ooth (B oston U niv.), Sekhar C h ivukula (B oston U niv.), M arcus P rice (U niv. o f N ew M exico), S idney R u d o lf (U niv. o f U tah), W illiam Skocpol (B o sto n U niv.), an d T. A. W iggins (P ennsylvania State U niv.). I am also indebted to several students w h o have

read an d critiqued the tex t, esp ecially Ian G oepfert, Eric H aw k, and Jo h n Ross. It is a p leasu re to acknow ledge th e ex p ert contribution m ad e b y the s ta ff o f Jo h n W iley & Sons, especially C lifford M ills (physics acquisition editor), C athy D onovan (editorial assistant), Ju lia S alsbury (editorial assistant), K ath a rin e R u b in (se n io r p ro d u c tio n e d ito r), Ish a y a M o n o k o ff (illustration), Jaim e Perea (illu stratio n coordi­ nator), S tella K upferberg (photo research), H ilary N ew m an ( p h o to r e s e a r c h ) , A n n B e rlin ( p r o d u c tio n ) , P a u l C onstantine (digital p ro duction), Jen n ifer D ow ling (d ig i­ tal p ro duction), K evin M urphy (designer), and C athy F aduska (m ark etin g m anager).

J a m e s W i llia m R o h l f B r o o k lin e , M a s s a c h u s e tts

CONTENTS

CHAPTER 1 Survey o f Particles and Forces 1-1 D isc o v ery o f A tom s

3-2 T h e T h e rm a l R a d ia tio n S p e c tru m

1

2

3-4 A to m ic S p e c tra a n d th e B o h r M odel

1-2 C lassica l E le ctro m a g n etism

CHAPTER 4 Special Relativity

1-4 L o o k ing In sid e tfie N ucleu s: P ro to n s a n d N e u tro n s 16 1-5 M ass a n d B in d in g E n erg y

1-7 P r o p e rtie s o f th e F o u r F o rc e s

98

4-1 F o u n d a tio n s o f S p ecial R e la tiv ity

17

1-6 A tom s o f th e T w en tieth C e n tu ry : Q u a r k s a n d L e p to n s 20 21

122

127

CHAPTER 5 Wave P roperties o f Particles and The U ncertainty Principle 135

34

2-2 T e m p e ra tu re a n d the Id e a l G as 41 2-3 T h e M ax w ell-B o ltzm an n D istrib u tio n

125

4-6 D isco v ery o f th e P o s itro n

33

102

4-3 R e la tio n sh ip B etw een E n e rg y a n d M o m en tu m 112

4-5 C o m p to n S c a tte rin g

CHAPTER 2 D istribution Functions and k T

99

4-2 R e la tio n sh ip B etw een S p ace a n d T im e

4-4 F o u r-V ecto rs

2 -4 D en sity o f S tate s

82

7

1-3 L o o k ing In sid e th e A tom : E le c tro n s a n d a N u cle u s 9

2-1 D is trib u tio n F u n c tio n s

66

3-3 Q u a n tiz a tio n o f E le c tro m a g n e tic R a d ia tio n 76

46 5-1 D eB roglie W av elen g th

55

136

5-2 M e asu rin g th e W ave P ro p e rtie s o f th e E le c tro n 140

CHAPTER 3 P lanck’s Constant

5-3 P ro b a b ility A m p litu d es

61

3-1 A tom s a n d R a d ia tio n in E q u ilib riu m

143

5-4 W ave D e sc rip tio n o f a P a r tic le 62

147

5-5 C o n seq u en c es o f th e U n c e rta in ty P rin c ip le 153

vii

CHAPTER 6 R utherford Scattering

CHAPTER 9 Beyond the H ydrogen Atom

162

6-1 M e a su rin g S tru c tu r e b y P a rtic le S c a tte rin g 163 6-2 D efin itio n o f C ro ss S ection

253

9-1 In d e p e n d e n t P a r tic le A p p ro x im a tio n 9-2 T h e P a u li E x clu sio n P rin c ip le

166

254

9-3 Shell S tr u c tu r e a n d th e P e rio d ic T ab le

6-3 P ro b in g th e S tru c tu r e o f th e A tom

168

6-4 P ro b in g th e S tru c tu r e o f th e N u cleu s

9-4 T h e C o u p lin g o f A n g u la r M o m en ta

176

6-5 P ro b in g th e S tru c tu r e o f th e P ro to n

179

6-6 P ro b in g th e S tru c tu r e o f th e Q u a r k

183

6-7 S u m m a ry o f th e S c a tte rin g E x p e rim e n ts

CHAPTER 7 The S chrodinger Equation

9-5 E x cited S ta te s o f A tom s

261

264

185

268

CHAPTER 10 M olecules and M olecular Spectra 10-1 T h e H y d ro g e n M olecule

192

10-4 M o le cu lar S p e c tra

7-3 F in ite S q u are-W e ll P o te n tia l 7-4 B a r r ie r P e n e tra tio n

200

7-7 T im e -D e p e n d e n t S c h ro d in g e r E q u a tio n

216

CHAPTER 11 * The Nucleus 296 11-1 D isco v ery o f th e N e u tro n

297

11-2 B asic P r o p e rtie s o f th e N u cleu s

221

11-3 N u c le a r M odels

8-2 S e p a ra tio n o f V aria b les

223

11-5 N u c le a r R e ac tio n s

226

8-3 T h re e Q u a n tu m N u m b ers

227

8-4 In trin s ic A n g u la r M o m en tu m 8-5 T o ta l A n g u la r M om entum

11-6 N u c le a r S p in

305 315

319

11-7 T h e M o ssb a u e r E ffect 236

300

303

11-4 R a d io a c tiv e D ecays 8-1 T h e G ro u n d S ta te S o lu tio n

322

11-8 P assa g e o f R a d ia tio n th ro u g h M a tte r

239

8-6 T h e S p in -O r b ita l In te ra c tio n : F ine S tr u c tu r e 241 8-7 A tom ic T ra n sitio n s a n d S election R u les

8-9 T h e L am b S h ift

291

209

7-6 S c h ro d in g e r E q u a tio n in T h re e D im ensions 213

8-8 T h e Z eem an E ffe ct

290

10-6 A b s o rp tio n S p e c tru m o f W a te r

7-5 Q u a n tu m H a rm o n ic O scilla to r

245

CHAPTER 12 Q uantum Statistics

333

246 247

280

287

10-5 A b s o rp tio n fro m C, O p h iu c i

207

CHAPTER 8 The H ydrogen Atom

279

10-3 M o le c u la r V ib ra tio n s a n d R o ta tio n s

193

276

277

10-2 T h e S o d iu m -C h lo rid e M olecule 7-2 P a r tic le in a B ox

255

9-6 A tom s in a n E x te rn a l M ag n etic F ie ld

191

7-1 F re e - P a rtic le W ave E q u a tio n

254

12-1 P a r tic le D istin g u ish a b ility 12-2 B o so n s 12-3 F e rm io n s

334

336 338

12-4 S c a tte rin g o f Id e n tic a l F e rm io n s a n d B o so n s 340

326

CHAPTER 16 High-Energy Physics: The Gadgets

12-5 C o m p a riso n o f th e D istrib u tio n F u n c tio n s 341 12-6 D en sity o f S tate s

341

12-7 E x am p les o f Q u a n tu m D istrib u tio n s

16-1 P a rtic le A c c e le ra to rs

345

16-2 P a rtic le D e te c to rs

CHAPTER 13 Masers and Lasers

349

13-1 S u m m a ry o f P h o to n —A tom In te ra c tio n s 13-2 S tim u la te d E m issio n o f R a d ia tio n 13-3 A m p lificatio n o f R a d ia tio n 13-4 T h e A m m onia M a se r

350

CHAPTER 17 High-Energy Physics: Classification of the Particles 472 17-1 D iscovery o f th e M esons

355

17-3 T h e A n tip ro to n

359

17-5 L eptons

375

14-3 H e a t C a p a c ity

378

144. O h m ’s L aw

492

CHAPTER 18 High-Energy Physics: Unification o f the Forces 501

370

18-1 F ro m Q u ark s to Q u a n tu m C h ro m o d y n am ics 502

384

14-5 S em ic o n d u cto rs

386

1 4 -6 T h e H a l l E f f e c t

393

CHAPTER 15 Superconductivity

478

489

17-6 H eav y Q u a rk s

CHAPTER 14 Conductors, Insulators, and Sem iconductors 369

14-2 F e rm i E n erg y

476

17-4 C lassificatio n o f th e H a d ro n s : th e Q u a rk M odel 480

357

14-1 E le c tro n ic E n erg y B a n d s

473

17-2 Q u an tu m N u m b e rs o f th e P io n

355

13-6 E x am p les o f L a se rs

440 451

352

1 3 -5 A m p l i f i c a t i o n a t I n f r a r e d a n d O p t i c a l

W avelengths

439

18-2 Q u an tu m T h e o ry o f th e W eak In te ra c tio n 507 18-3 U n ificatio n o f th e F o rc e s

403

15-1 B a sic E x p e rim e n ta l P ro p e rtie s of S u p e rc o n d u c to rs 404

CHAPTER 19 The Early Universe

532

19-1 T h e D a rk N ight Sky

533

19-2 O verview o f th e U n iv e rse

15-2 D ev e lo p m e n t o f th e T h e o ry of S u p e rc o n d u c tiv ity 412

19-3 E v o lu tio n o f th e S ta rs

15-3 F u r th e r P ro p e rtie s o f S u p e rc o n d u c to rs 1 5 4 H ig h -7 c S u p e rc o n d u c to rs

525

544 548

19-5 T h e Physics o f th e E x p a n d in g U n iv e rse

430

15-5 A p p lic atio n s o f S u p e rc o n d u c tiv .ty

420

19-4 T h e Role o f G ra v ity

534

433

551

APPENDIX A Physical Constants

APPENDIX B Maxwell’s Equations APPENDIX C Vector Calculus

APPENDIX H The Hydrogen Atom

570

572

APPENDIX D D istribution Functions APPENDIX E Spherical C oordinates

APPENDIX I Fam ous Experim ents in M odern Physics 597 APPENDIX J Outstanding Problem s

576

592

600

578

APPENDIX K N uclear D ata

587

APPENDIX L Table of P article P roperties

602

Answers to Selected Problem s APPENDIX F The Taylor Expansion

589

Example Index Subject Index

APPENDIX G Transform ation o f Electric and Magnetic Fields 591

633 637

624 631

CHAPTER

1

SURVEY OF PARTICLES AND FORCES I f in so m e c a ta c ly sm , a ll o f s c ie n tific k n o w le d g e w e re to b e d e s tro y e d , a n d o n ly o n e s e n te n c e p a s s e d o n to th e n e x t g e n e ra tio n s o f c r e a tu r e s , w h a t s ta te m e n t w o u ld c o n ta in th e m ost in fo rm atio n in th e fe w e st w o rd s? I b e lie v e it is th e a to m ic h yp o th esis (o r th e a to m ic f a c t , o r w h a te v e r you w ish to c a ll it) th a t a il th in g s are m a d e o f a to m s— little p a rticle s th a t m ove a r o u n d in p e rp e tu a l m o tio n , a ttr a c tin g ea c h o th e r w h e n th e y are a little d ista n c e a p a rt, b u t re p e llin g u p o n b e in g sq u eezed in to o n e a n o th e r. In th a t one s e n te n c e , y ou w ill s e e , th e re is a n e n o rm o u s a m o u n t o f in fo rm a tio n a b o u t th e w orld, if ju s t a little im a g in a tio n a n d th in k in g a r e a p p lie d .

Richard P. Feynman 1-1 DISCOVERY OF ATOMS 1-2 CLASSICAL ELECTROMAGNETISM 1-3 LOOKING INSIDE TH E ATOM: ELECTRONS AND A NUCLEUS 1-4 LOOKING INSIDE TH E NUCLEUS: PROTONS AND NEUTRONS 1-5 MASS AND BINDING ENERGY 1-6 ATOMS OF TH E TW ENTIETH CENTURY: QUARKS AND LEPTONS 1-7 PR O PE R T IE S OF TH E FOUR FORCES

M atter is m ade o f atom s. T h e properties o f atom s are quite rem arkable. C onsider an ordinary rock. T ry pulling the atom s in a rock ap art o r squeezing them together. It is not easy to d o so! T h e atom s in the rock are rem arkably stable. T h e discovery o f atom s and the m easurem ent o f their pro p erties have p av ed the w ay for our present understand­ ing o f the universe. The idea o f m atter being com posed o f atom s is the single m ost im portant concept in all o f science. T h e atom ic com position o f m atter explains such apparently diverse phenom ena as w hy the sky looks blue, w h y a rock feels hard, w hy a rose sm ells fragrantly, why a violin sounds m ellow , an d w hy a lim e tastes sour. O ur story o f m odem physics begins by tracing the im portant ideas and experim ents leading to the discovery o f atom s.

1-1 DISCOVERY OF ATOMS A bout 2400 years ago, the G reek philosopher A naxagoras invented the idea th at m atter w as com posed o f tiny invis­ ible seeds, or sperm ata. T his concept w as expanded a few years later by D em ocritus, w ho called the indivisible p articles o f m atter atom s . T h e atom ic hypothesis had its renaissance in the nineteenth century a s scientists m ade the fam ous classification o f the elem ents in the form o f the periodic table. T he idea o f explaining the properties o f a com plex object w ith elem entary building blocks has sur­ v iv ed from the ancient G reeks into m odem science. We know that m atter is com posed o f atom s because w e have d eveloped the experim ental techniques needed to test the atom ic hypothesis. T he ancient G reeks did not have the necessary experim ental tools; this is w hy there w as no advance in the understanding o f atom s for m ore than 2000 years!

o f the o th er elem ent need ed to m ake the two com pounds m ust b e in the ratio o f tw o sm all integers. T h e D alton atom ic theory w as q uickly proven to b e correct by experi­ m ent. (F o r exam ple, 16 g o f oxygen com bines w ith 12 g o f carbon to form carbon m onoxide an d 32 g o f oxygen com bines w ith 12 g o f carbon to form carbon dioxide. The ratio o f oxygen m asses need ed to m ake the tw o co m ­ pounds is 2/1.) T his result is know n as the la w o f m ultiple pro po rtio ns. A ccording to the theory o f Dalton, each elem ent w as assigned an in teg er atom ic mass num ber (A). Scientists o f the early nineteenth century faced the form i­ dable problem o f d eterm ining both the atom ic m asses o f the elem ents and the chem ical form ulas o f com pounds. A great leap forw ard in the understanding o f the struc­ tu re o f m atter w as m ade in 1811 by A m edeo A vogadro. A vogadro correctly hypothesized th at th e particles o f a g as w ere sm all in size com pared to the distance betw een the particles. A vogadro determ ined that the particles o f the gas w ere often m ad e up o f m ore than one atom bound together into m olecules and th at at a fixed tem perature and pressure, equal volum es o f a gas contained equal num bers o f m olecules. T his im portant result, w hich will be d is­ cussed in m uch m ore detail in C hapter 2, is the basis o f the id e a l ga s law. T he m o lecu la r m ass num ber is d efined to be the sum o f

the atom ic m ass num bers o f the atom s th at m ake up the m olecule. R elative m olecular m ass num bers o f co m ­ pounds w ere determ ined by m easuring the m asses o f equal volum es o f gases at fixed tem perature and pressure. T ogether w ith the assum ption that the sim plest m olecules contained only one atom o f certain elem ents, the discov­ ery o f A vogadro p rovided a system atic m ethod for m ea­ surem ent o f the atom ic m ass num bers.

The Periodic Table Atomic Mass Numbers The experim ental foundation o f the atom ic theory is the la w o f definite proportions'. W henever a given com pound is form ed from two elem ents, the ratio o f the com bining m asses o f the elem ents is observed to be a constant. T his resu lt holds for every com pound although the m ass ratio is different for each com pound. I f a com pound is m ade up o f m ore than tw o elem ents, then the ratio o f m asses o f any tw o elem ents is constant. In 1807, John D alton postulated that atom s o f each elem ent had a unique m ass. D alton’s atom ic theory con­ tained a sim ple prediction for the case w here the sam e two elem ents com binc to form tw o different com pounds: For a given m ass o f one o fth e com bining elem ents, the m asses

In 1869, D m itri M endeleev m ade the first classification o f the elem ents according to their chem ical properties and their atom ic m ass num bers. T he elem ents w ere ordered w ith increasing atom ic m ass n u m b er and placed in several colum ns according to their chem ical properties. Starting w ith hydrogen, an integer serial num ber w as assigned sequentially to each elem ent. T his serial num ber is called the a tom ic num ber (Z). For hydrogen Z = 1, for helium Z = 2, an d so on. In his periodic table, M endeleev discovered som e gaps that allow ed him to correctly pred ict the exist­ ence o f undiscovered elem ents, the ultim ate goal o f a theoretician! T he m issing elem ents w ere soon discovered. A ll w as fine w ith the periodic table until W illiam R am say and Lord R ayleigh discovered the elem ent argon in 1894.

1-1 DISCOVERY O F ATOMS

A rgon h ad no place in th e theoretical classification o f the elem ents; such a discovery is th e ultim ate goal o f an experim entalist! T he perio d ic table w as m odified by ad d ­ ing a w hole ex tra colum n to accom m odate argon and other in ert g ases that w ere soon discovered. A ll the great ad­ vancem ents in science have been m ade through such interplay b etw een theory an d experim ent. T he m odern p erio d ic table o f th e elem ents is show n in F igure 1-1.

Avogadro’s Num ber O nce th e atom ic m ass num bers o f th e elem ents w ere k n o w n , scientists h ad a very pow erful atom ic relationship: T h ere are equal num bers o f atom s in A gram s o f any elem ent, w here A is th e atom ic m ass n u m b e r o f the elem ent. F or exam ple, 1 g o f hydrogen, 12 g o f carbon, and 238 g o f uranium all co n tain th e sam e n um ber o f atom s (see F igure 1-1). T he n um ber o f atom s in A gram s o f any e lem en t is called A vo g a d ro 's n um ber (NA). T he quantity o f m atter com prising A v o g ad ro ’s n um ber o f atom s is called one m ole. T he n ex t g reat experim ental challenge w as to d eterm ine the value o f A v o g ad ro ’s num ber. Ju st h o w m a n y ato m s are th ere in o n e g ra m o f hydrogen?

M easuring th e Size o f an Atom C onsider th e m easurem ent o f the size o f an object using lig h t as a probe. Suppose that th e o b je ct to b e m easured is th e w idth o f a narrow slit, as illustrated in F igure 1-2. R ays o f lig h t are allow ed to p ass through th e slit, an d the in ten sity o f th e light is m easured a t a large distance from th e slit. T h e im age o f the narrow slit is not infinitely sharp becau se th e ray s o f light bend o r diffra ct on passing th ro u g h the slit. D iffraction is a fundam ental p roperty o f w aves. T h e location o f th e m axim a and m inim a o f the d iffraction pattern m ay be deduced by tracing rays o f light th ro u g h th e slit. D estructive interference occu rs w hen rays h av e path lengths th a t differ by an am o u n t (AL ) equal to o n e -h a lf o f th e w avelength o f th e light rays (A,ighl):

M =

(1.1)

A lighl = d s i n 0 min.

3

(1 .3 )

M easurem ent o f 0 min determ ines th e size d o f th e slit. T he sharpness o f th e in ten sity p attern, w hich is_govcrned by diffraction, is directly proportional to th e w avelength o f the light. F o r Alight= d , 9mia= n i l and destructive interference is n o t m easurable. W e can n o t m easu re th e size o f th e slit u sin g light that has a w avelength larger th an th e size o f the slit. F or this case, all w e can exp erim en tally determ ine is an upper lim it on th e slit size, d < A,ighI. A s a resu lt o f diffraction, m easurem ent o f the size o f an object is lim ited by the w avelength o f th e light used in the m easurem ent. T w o points separated by a distance d can be resolved only i f the w avelength o f the light does n o t exceed d. A consequence o f th is is th at a single atom cannot be resolved w ith an ordinary m icroscope. This has nothing to do w ith th e quality o f th e m icroscope, b ut rather w ith the fundam ental lim it im posed by diffraction. T h e w avelength o f light, defined by th e sensitivity o f th e eye, is in the range 400 nm < / l ligh, < 700 n m .

(1.4)

O n e n an o m eter (nm ) is equal to 10"9 m eters. T h e diam eter o f an atom (d„om) is m uch sm aller th an th e w avelength o f light: ^ a ,o m

«

^ -lig h ,-

( 1 -5 )

T h e m icro sco p e wax used, h ow ever, to m ak e th e first d eterm ination o f th e size o f an atom ! T his grew o ut o f the d iscovery in 1828 by R obert B ro w n th at sm all particles su sp en d ed in a liquid h av e a sm all b u t m easurable random m otion. T his B row nian m o tio n is caused b y m o lecu les o f th e liquid co lliding random ly w ith th e suspended p a r­ ticles. T h e av erag e d isp lacem en t as a function o f tim e d epends on th e rate at w hich m olecules strike th e sus­ p en d ed p article. T h e rate a t w h ich th e m o lecu les strike th e suspended p article d epends on th e n u m b er o f m o lecu les in th e liquid. In 1905, A lb ert E instein published a fam ous pap er on the m olecular theory ofheat. From his m olecular theory, Einstein deduced a form ula fo r th e tim e (?) dependence o f the average displacem ent (R) o f a sphere o f know n radius (r0),

I f th e w idth o f the slit is d, th en the p ath length difference is related to th e angle a t w hich th e intensity is a m inim um R =CJ tT -> vV o

($» J by ^

= f s i n 0 n,in-

C om bining th ese resu lts gives

( 1-2)

(!•« )

w h ere C is a constant fo r a giv en liquid a t a fixed tem p era­ ture. (T he m eaning o f tem p eratu re is an im portant concept th at is th e su b ject o f C hapter 2.)

Periodic Table of the Elements ' 1

1.01 hydrogen

a t o m ic

a t o m ic

n u m b e r (Z )

m ass M )

12

4 .0 0 helium

H

He

0 .07 0 8 3

nam e

6 .9 4

4

lithium

beryllium

Li

Be

0 .5 4 2

1.82

111

2 3 .0

sodium

i 12

I

boron

d e n s it y ( 1 0 3 kg/m 3)

2 4 .3

13

7

12-0

!

carbon

14.0 nitrogen

F l.ll

28.1

15

3 1 .0

Si

P

2 .7 0

2.33

1.82

calcium

‘

22

45.0

scandium

4 7 .9

titanium

23 ,

50.9

vanadium

5 2 .0 :2 4 J chromium

25

54.9

2 6

' manganese

5 5 .9

2 7

58.9

iron

cobalt

:2 8

58.7

(2 9

6 3 .6

3 0

6 5 .4

31

Ne

0 1.14

14

6 9 .7

nickel

copper

zinc

gallium

!3 2

7 2 .6

16

phosphorous

!3 3

| germanium

|17

sulfur

:

1.21

3 5 .5

s

Cl

Ar

2.07

1.56

79.0

‘ 35

selenium

1.40

79.9

Kr

So

Ti

V

Cr

Mn

Fe

Go

Ni

Cn

7n

Ga

Ge

As

Sfi

Rr

1.53

2 .9 9

4.51

6.09

7 .1 9

7.47

7.87

8.9

8.91

8 .9 3

7.13

5.91

5.32

5.77

4.81

3 .1 2

1

strontium

3 9

8 8 .9

j41

yttrium

zirconium

niobium

9 5 .9 42 molyodenum

4 0

9 1 .2

9 2 .9

143

98

technetium

4 4

101

45

< ruthenium

103

rhodium

46 105 . palladium

4 7

108

4 8

silver

;

H2

4 9

cadmium

"5

50

51

119

122

52

128

indium

tin

antinomy

tellurium

Rh

Sr

Y

Zr

Nh

Mn

Tn

Rli

Rh

Prl

In

Sn

Sh

Tfi

2 .5 8

4 .4 8

6.51

8 .5 8

10.2

11.5

12.4

Ag

Od

1.63

12.4

12.0

10.5

8 .6 5

7.29

5 .7 6

6 .6 9

6 .2 5

133

cesium

56

137

barium

71

175

72

178

73

181

184

74

'7 5

186

j76

190

lutetium

hafnium

tantalum

tungsten

rhenium

osmium

77

192

iridium

178

195

79

197

8 0

201

81

204

8 2

207

platinum

gold

mercury

thallium

lead

8 3

209

8 4

W

Re

Os

lr

Pt

Au

Hg

TI

Pb

Bi

Po

16.7

19.3

21.0

2 2 .6

2 2 .6

2 1 .5

19.3

14.3

11.9

11.3

9 .8 0

9.31

Fr

Rat

260

unnilquadium

unnilpentium

263 106 unnilhexium

unmlseplium

Unq

Unp

Unh

Uns

104

Lr

;

261

57

139

105

;5 8

| lanthanum

L anthan ide series

1" A c tin id e series

140

cerium

!59

141

:-.is

i.r-

107

60

262

144

: neodymium

La

Ce

Pr

Nd

6.17

6 .7 7

6 .7 8

7.00

89

i

262

9 0

227

actinium

i

232

thorium

Ac

Th

10.1

11.7

91

2311

protactinium

Pa j 15.4

9 2

238

i 108

265

1 0 9

Une

Uno

61

145

6 2

‘ promethium

237

150

samarium

Pm i 93

266

unnilennicrri

! unniloctium

:

;6 3

152

{ europium

159

terbium

66

153

Gd

Tb

Dy

5.24

7.89

8 .2 7

8 .5 3

94

244

Pu

Am

20.5

19.8

11.9