Handbook of Elementary Physics (Russian Monographsand Texts on the Physical Sciences)

is SJ:i~on~~ctor\~re substances whme electrical conductivity . . 0 e mo Ion of bou~d electrons and whose resist~VI\~. at room teJ.llperature lIes within the range from 10- 2 ms cm. 1he resistiVity of semiconductors is stroncrly to e~~~r~ ure-dependent. In contradistinction to metals the f~~ISt~vlty of semiconduc~ors. decreases with an incre2~e in stronglyperattuhre. The reslst!vlty of semiconductors depends on e presence of Impurities.

°r

(4,44)

.,

where A' is a constant which is different for different met· als, T - the absolute temperature, k -' Boltzmann's con· stant (see p. 58) and e ~ 2.72 is the base of the natural loga· rithms. The quantities A' and

Fig.. 42. Electron energy level dIagram of scrniconduetor.

Electrons in matter are distributed about the atomic in such manner that any atom may po 1 a dls.crete s~t of energy values. Every electron c~~e~c~uIl~Y certam defiIllte energy levels, which are different from- t~l~ enen5Y levels of other electrons. These energy levels dre called c:llowed levels. The allowed energy levels fall . I two .reglOns, or band~, .which are separated by the s~.ca\?:~~ forb~dden gap contalIllng the values of elll'rgv which a;c forbidden to t.he electron. At the temperature"(PK :ill th,' electrons are !n the band ~f lowest cuclgil':i. and all (h~ energy: levels 1Il thiS iJ:l1ld will he occupied (Fig. 42). This band IS called the valencG band The .ecoml baud (the connuc~ei

8*

116

CH. IV. ELECTRICITY

duction band) of the non-metallic elements does not contain a single electron at O"K. In metals the conduction and the valence bands overlap. The energy required for an electron to pass from the valence band to the conduction band is called the width of the forbidden gap PEn). Semiconductors possess either electron (n-type) or hole (p-type) conductivity. Electronic conductivity is due to the motion of the electrons in the conduction band; hole conductivity is due to electrons in the valence band moving from one atom to another which has "lost" an electron to the conduction band. The motion of an electron in the valence band is eqUivalent to the motion of a positive charge in the opposite direction. Such a positive charge is termed a "hole".

TABLES AND GRAPHS for light ra~n - 10-" to 10-:-' CGSE units of current'cm' ,·'t tll11 S

thunde! storms : and ! hail - UI' 3x 10-'. C'GSE' renftorre m , ' to ,

ET=a (T 1

-

The quantity a is called the di(Jerential thermal e.m.f. (or the coefficient of the thermal e.m.!.); it is numerically equal to the thermal e.m.!. developed per degree centigrade.

[ cur-

Table 69 Resistivity and Tempe ra t ure Coe ftl· clent of ResistiVity of Metals Metal

T 2 )·

0

The current in a lightning stroke mo,' I . . (the most common values are '[rom 20 "<)0 let .1.S1 high
5. Thermoelectricity If a closed circuit is composed of two dissimi lar metals and the junctions of the metals are maintained at different temperatures, a current will flow in the circuit. This current may be attributed to a thermal e.m.f. developed at the junctions, and the phenomenon itself is called the thermoelectric e(Ject. Within a certain temperature range the magnitude of the thermal emf. is approximately proportional to the temperature difference. In this case

117

Aluminium Brass . . • Chromi um Copper

Iron . . . Lead " Mercury Molybdenum Nickel .. Phosphor bronze Silver . . . Tantalum. Tin . . . . Tungsten . Zinc . • • . . . . . . . . . . . . .

I(csistivity at :!(PC ohm mm;jm

00210 0.025·0.00 0.027 0.0 i 75 0.098 0.221 O. ~)58

0.057 0.100

0.015 0.0 I 0 o .155

0.115 0.055 O.05~

Temperature coefficient

at

~occ

0,0049 0.OCi2·0.00 7 (J.()039 0.0002 () ,0011 (1.0009 0.0033 0.0050

0.0040 0.003G 0.0031 0.0012 0.0045 0.0035

TABLES AND GRAPHS

Electric Currents and the Earth's Atmosphere JverI.• (due to the motion of positive and negative ions in the atmosphere) is The experimentally measurad density of the vertical current jvert:.--:..:2~<10-t(j amp/cm

2

•

The density of lie ('mrents due to tbe Illotion 01 charged raindrops, snowflakes and bail is:

Note. The valucs given in the table are average values' for cliffe

~~~t samples they depend on the degree of purity. the;rnal' treatment: to nke7~~6erat,!re coefficient of resistivity of pme metals is cl05e exp,;nsi 0-;;- 0'log2le:: I.e.. to t he val ue of the ceJefli ci ent of t herma]

j! \)

TABLES AND dRAPES 118

CH. IV. ELECTRICITY

Table 71

Table 70 Transition Temperatures to the Supercondueting state for Some Metals Substance

1>1 etals Zirconi um Cadmium Zinc Aluminium Uranium Tin Mercury Tantalum Lead Niobium

ITranSitiOn temperatu- II re, 0 K.

0.3 0.6 0.8 1.2 1.3 3.7 4.1 4.4 7.3 9.2

A!lo!J s

Bi -pt Pb·- Au Sn _. Zn Pb -Eg.

,

0.16 2.0-7.3 3.7 4.1-7.3

Substance

Sn - Hg. Pb -J\.g. Pb -Sb. Pb -Ca

I

Transi lion temperature, oK

Alloys

4.2 5.8-7.3 6.6 7.0

(58.8% Constantan Cu, 40% Ni, 1.2% Mn) Fechral (80% Fe, 14 'It, Cr, 6% AI) . . . . . German silver (65% CU.20%Zn,15%Ni) Mangani n (85% Cu, 12% Mn, 3% Ni) Nickeline (54% Cu, 20% Zn. 26% Ni) Nichrome (67.5% Ni, 15% Cr, 16% Fe. 1.5% Mn) (84% Cu, Rheostan 12% Mn, 4% Zn) •

COIl/pounds

Ki Hi PbSe SrDi, KbB MoC

Nb 2 C NbC. J\bN V,Si. J\b,Sn.

Alloys of High Ohmic Resistance

4.2 5.0 5.5 6 7.6-8.3 9.2 10.1-10.5 15-16 17.1 18

, Notes. 1. There are a number "f ,uperconducling alloys containing a greater number of components: I(ose's metal (8.5°K), Newton's metal (8.5 C K), Wood's metal (8.2°K), Pb - As - Bi (90 0 K), Pb - As- Bi -Sb (9.6°K)· 2. Upon transition to the superconducling state the resistivity of compounds and alloys varies throughout a wide range of temperatures (sometimes as wide as 2°K). In addition the transition temperature depends on the heat treatment of the alloy or compound. In such cases the table indicates the bounds within which the transition temperat ure Ii es,

Resi sti vity at 20°C, ohm mm 2 /rn

Temperature coefficient (in the range 0-100°C)

Maximum operating temperature, °C

0.00001

500

0.0001

900

0.44-0.52 1.1-1.3 0.28-0.35

0.00004

150-200

0.42-0.48

0.00003

100

0.39-0.45

0.00002

150-200

I. 0-1. I

0.0002

1,000

0.45.0.52

0.0004

150-200

Note. The value ot the temperature coefficient of resistance of constantan varies from --0.00004 to +0.00001 depending on the sample. The minus sign before the temperature coefficient denotes that the resistance decreases with increasing temperature.

Table 72 Allowed Current-Carrying Capacity of Insulated Wires for Prolonged Operation (amp)

~. area, mm 2

1

1.5

2.5

4

6

10

i4 \1

20 16 8

25 20 10

31 24

43 34 17

16

25

75 60 30

100 80

Material

Copper . , Aluminium Iron.

11 8 -

-

12

II

-

CH. IV. ELECTRICITY

120

Table 73

~~l~

~esistivity of Electrolytes at 18°C and Different

Concentrations (see Fig. 43) Concenlra-

Solute

tion.

%

!
Tem perature coefficient. x (degree-I)

Ammon! um chloride, NH.Cl

5 10 20

10.9

5.6 3.8

0.0198 0.0186 0.0161

Copper sulfate, CuSO,

5 10 17.5

52.D 31.5 23.8

0.0216 0.0218 0.0236

Hydrochloric acid, HCI

5 20 40

2.0 1.3 I.D

0.0158 0.0154

Nitric acid, HN03

10 20 30 40

2. I 1.5 1.3 1.1

0.0145 0.0137 0.0139 0.0150

Sodium clilori de, NaCI (com man sall)

5 10 20

14.D 8.3

5.1

0.0217 0.0214 0.0716

;).1 3.2 3.0 8.3

0.0201 0.0217. o .0299 0.0648

4.8 1.5 1.1

1.5

0.0121 0.0145 0.0162 0.0178

52.4 31.2 21.2

0.0225 0.0223 0.0243

Sodium hydroxide. NaOH

5 10 20 10

~t\

o~ /C

Fig.

Zinc sulfate, ZnSO,

5 20 30 40

10 20

20

43.

t

YO 40 50';;-·---=jC;;O......,7.t: ... O.......,gf:. O.......,gf:.O,... COllce;;/;-c//oJ1, % ,

ConcenLr<.iUoll dependence

of resistivity qf aqueous 0olutioll of H,SO,.

Table 74 Thermal Electromotive Force of Some Metal Couples in Millivolts Junction tem-l Plati num, platinum perature, °C with 10% rhodi LIm

-200

lOa

Sulfuric acid, H,SO,

121

TABLES AND GRAPHS

-

Note. The resistivity of electrolyle falls off with increasing temperature (as distinct from metals): The resistivity for other lemperatures Pt can be computed from the formula (compare with (4,25)): P =?IR[I -x (t-18)]. where x is the temperature coefiieient given i~ the table, 0,< - the resistivity at 18°C, t - the temperature for which the resistivitY!t is sought.

200 300 40 a 500 (jO 0 700

ROO 1,000 1,500

I

Iron,

Copper.

constantan

constantan

R O.li!

1.44 2.32 :1.25 4.22 5.22 G.2li 7.33 9.57 15.50

5 11 16 2:2

27 33

5.5 I 9

15 21

~j9

Iii 58

Note. The temperature of the 1'o[or,,,,,'o junction is kept at

O'c.

122

CH. IV. ELECTRICITY

TABLES AND GRAPHS

Table 75 Differential Thermal e.m.f. (:1) with Respect to Platinum at oDe Metal

Antimony Bismuth . Constantan

",

Metal

p.v/degree

7.4 16.0 -16.4

Copper

47.0 -65.0 -34.4

Iron

Nickel

Table 76 Electrochemical Equivalents

-,

p.v/degree

Note. The minus signs indicate that the current In the hot junction flows from the metal with the smaller algebraic value of ... For example, in the thermocouple copper·constantan (Fig. 44) the current in the hot junction flows !rom constantan to copper.

123

Ion

H+

I

Gram chemical equivalent

K, mg/coul

1.008

Ion

Gram chemical equivalent

K, mg/coul

I 0.0104

CO;-

30.0

0.3108

0-Al++ + OH-

8.0 9.0 17.0

0.0829 0.0936 0.1762

Cu++ Zn++

Cl-

31.8 32.7 35.5

0.3297 0.3387 o .3672

Fe++ +

18.6

0.1930

SO 4 - -

48.0

0.4975

20.1

0.2077

0.642

0.2388 0.2895

NO; Cu+ Ag+

62.0

23.0 27.8

63.6 107.9

0.l\590 1.118

Note. The number of pIllS or minus signs In the superscript denotes the number of elementary charges carried by one ion.

Table 77

/0 '\

o

lOO

.iOO

';'00

Absolute Normal Potentials of Some Metals

1100 tot. ,I

Fig. 44. Temperature dependence of difjerential thermal e.m.f. of copper·constantan thermocouple.

Metal

Cadmium Chromium Copper Iron Lead

I

Normal poten·11 hal, v

-0.13 -0.29 0.61 -0.17 0.15

Metal

Manganese Mercury Nickel Silver Zinc

INormal patential, v

-1.28 I. 13 0.04 I. 07 ·-0.50

TABLES AND GRAPHS

124

125

CH. IV. ELECTRICITY

Charging and Discharging Accumulators

Table 78 e.m.f. of Electrochemical Cells Name of cell

Negative clec t rode

Posi ti ve eleel rode

Daniell

Zinc

Copper

Solution

e.m.f.. v

Di fferent solutions at electrodes: zinc immersed in solution of slIlfuri c acid (5-10%); copper immersed in saturated solution of copper sulfate CuSO,

1.1

a)

Edison

Powdered i rOll (or cadmium mixed \vi th i rOil

20(%

J'\ickcl

solution

Z5 2.4 "'2.2.

~

~2..0

~

::;;: 1.8

1.4-1.1

of

potassium hydroxide (KOH)

dioxide

Zinc

Carbon

Lead accumulator

Spongy lead

Lead peroxide PbO,

Lec1anche

Zinc

Carbon

Solu ti on of salammoniac, manganese peraxi de wi th powdered carbon

1.46

Lec1anche (dry)

Zinc

Carbon

1 1 3 2

part ZnO. part KH,CI. parts gypsum. parts ZnC!, and water until a paste is formed

1.3

Zinc

Silver

Sollltion of si urn hydroxi de

Cadmium amalgam

27 - 2K % solution of H,SO" free from chlori nc, density 1.20

I

POLlS-\

I Mercury

2.01

12 parts K,Cr,O,. 25 parts I-IzSO h 100 parts If,O 1

1

Weston, normal

I {}

0.5

I

1.5

2.

i ..'

T/.r;;..D,J

Grenet

oxi de

f.O

/.4

oxide:;)

SI lver-zi nc accumulator

leM O'CCI/l7lI//iJ/or

2.8

2.0-1.9 at 15°C

1.5

(KOll)

Saturated solution of CdSO,. pas te of Ilg,SO, and CdSO,

1. 0183

J

.1.5

"

't.5 5

126

CH. IV. ELECTRICITY

TABLES AND GRAPHS

127

Table 79

Table 81

Mobility of Ions in Aqueous Solutions at 18°e Mobility, cm 2 ,'sec v

Anions

Mobility, cm 2 /sec v

Na+

0.003263 0.000669 0.000450

OHCiNO.-

0.00180 0.00068 0.00062

Ag+

0.00056

S04

0.00068

2n++

0.00048 0.00046

Cations

Mobility of Ions in Gases at 760 mm Hg and zooe (in cm 2 jsec v)

Gas H+

K+

Fa+++

CO;-

0.00062

Notes. I. Cations are positively charged. anions - negatively charged ions. 2. The ionic mobility increases approximately 2% per 1°C Increase In temperature. 3. The number of plus or minus signs in the superscripts Indicates the number of elementary charges carried by one ion.

Posi ti ve ion mobility

Negative ion mobility

1. 36

I. 87

1. 37 1. 37 0.76 5.09 6.3 1. 36

l. 51 I. 70 0.81 6.31 8.1 1.8

Air, dry . Air. saturated wi th water vapour Argon Ca rbon di oxi de Helium. Hydrogen . Oxygen .

Notes. I. The values of the mobili ty are given for the case of Ionisation by X·rays. 2. The mobility of ions in gases decreases with a rise in pressure and increases wi th the temperature.

Table 82 Table 80

Ionisation Potentials (in Electron-Volts)

Mobility of Electrons in Metals (in cmz/sec v) Ionisation process

MObility·····I 56/48144135130) 19/ 10 1 7 . 9 [5.8

Note. The field intensity inside metals actually does not exceed 0.001 v!cm; hence, the electron velocities will be numerically much smaller than the values of the mobility given in the table. This can easily be verified by means of the relation (4,23) by inserting thl! permissible values of the current density given in Table 72.

He Ne N2 Ar

-> He+ -> Ne+ -> N+2

-> Ar+ -> If; N --+N+ CO 2 -> CO; Kr -> Kr+

If,

I

Ionisation potential

Ionisation process

Ionisation potential

24.5 21.5 15.8 15.7 15.4 14.5 14.4 13.9

H -> H+ 0->0+ H"O -> H 2 O+ Xc -> Xe+ 0, -> 0; Hg -> Hg+ Na->Na+

13.5 13.5 13.2 12.8 12.5 10.4 5.1 4.3

I

K -> K+

~

TABLES AND GRAPHS

CH. IV. ELECTRICITY

128

129

Table 83

Table 86

Emission Constants of Some Metals and Semiconductors ~,

Element

ev

amp N,

i

C1ll2

dCg'rec2

II

Element

Aluminium

3.74

I"ickcl

Antimony

.:2.35 2.29 1.89 4.51 4.47

'Seleuium. iSilicon . . !Tcllurium

Barium Cesium.. Chromium Copper . . Germanium

lCiO 48

4.5() 4. ~H) 4.27

Iroll MolylH1cnul11

GO

I

..

4.84

iPlatinum'.

5.29 4.72 4.10 1.12 3.41

iT1JOri urn iTin... jTungsten IUrallium

-

N, amp

ev

cm:l degree

Substance 30 32

B C -graphite C - diamond Si Ge Sn. gray S Se, gray

70

4.11

60-100

4.50

~L74

Note. The work function depends markedly on the cJeanli ness of the surface and sped mens.

011

Properties of Most Important Semiconductors (see a Iso Figs. 46-49)

impurities. The figures in the table are for pure

Te I

Emission Constants of films on Metals

B~Tc~

PbSe ZnTe PbS AgBr CdTe Cu.,O AI;O,I ZnO

N,

Film

Tuuf(sten

Molybdenum

I', ev

amp cm 2 degree 2

1 .56 2.63 2.84 1.36 :J. 14 2.58 2.52

Barium Thari u m Uranium Cesium Lircollium TllOrlUm

Tantalum

1.5 3.0 3.2 3.2 5.0 1.5 0.5

-----------------'-------------Table 85 Emission Constants of Oxide-Coated Cathodes N, Cathode

Barium on nxidisccl tungsten

Nickcl- jJ"O - Sr 0 Barium -PI-Ni; BaO

O!l iJ

-- tt~Jl;:_C-;l(~11 --:->1'0 . . . . Jlil"kc} :J1loy

Thori um oxi de~coa ted (';\ t hade (meall value)

cv

amp cm:.l degree 2

I. I 0 1.20 I. :31 1 . :,7

0.3 0.96 0.18 2.45 0.OS7-2.18

~,

1 ';)1).\ .8:J 2.59

4.35

---~-----'------

I. \ 0.1 G-7 1.12 0.75 0.IJ8 2.4 2.3 0.:3(; 1.3 O. 17 0.2 0.25 0.3Ci

-

1 ,4 I 4 958 I 13 220

452

Mg2Sn

Element

Width of forbidden gap. ev

2,300

1 1:3 . .5 Do;) li70 585 778 1,OGS I ,240 1,1 14 4 :JO I 1045 1,2:J2

Ag,Te HgTe

Table 84

Melti ng poi nt, °C

2,050

Electron mobility, cm:!/sec

10

-

I

U.S O.G 1.2 1 .35 J .45 1.5-1. 8

1,975

2.5 3.2

I

1,800 1,90IJ 3,900 3,000 1,700 :!5 4,00IJ 10,000 600 200 1,400 IIJ() 650 35 450 .200

V

Hole mobility, cm 2/sec V

10

-

J ,200 500 1,900

-

--

1,200 100 150 150 1,400 800

-

\00 100 -

-

Notes. I. The values of the mobilities are given for room temperature and field intensities less than the critical field. Deviations from Ohm's law may occur, due to the field-depen_ dence of the mobility. The least intensity for which such deviations are Observed is called the critical field (Ecr)' At i=20°C the critical field in n-type p-type n- type p- type

germanium germanium si Ii con si Ii con

E cr =900 v/cm E cr =I,400 v,cm E cr =2,500 v!cm E cr =7,500 v:cm

The critical field decreases wfth decreasing temperature. 2. The wi dth 01 tbe forbi dden gap ill metals is of the order of 0.1 ev; ill dielectrics _ over 10 ev.

9

~1aK.

4,1)

CH. IV. ELEClRICITY

130

FUNDAMENTAL COXCEPTS AKD LAWS

131

SF!'e

PHe

~

__~ ..--.J

tl

]0 't--+-J-~J 1001L--~'---I!---l

100

T'K

JOO

200

j&"O--2Ju' - ~-JJO

N

~

FiiT. 49. Differential thermal e.m.f. versus lCll1!'C'ratlllc: a) Iced lelluride (upper C'urve--concentration of impuril"y
JO'~:---::o.oJ..'O-f--O-lOO-Z--Ij--!" 'g Fig. 46. Dependence of resistivity p on 1iT for intrinsic semiconductor, the

Fig. 47. Temperature dependellce of resistivi tv 01 g,,-'11Il
\&alues of p are plotted .on

the ordinate axi s on a garithmic scale.

10-

number of germ ani urn atoms, N - r.um 1.:ET of antimony Su atoms.

L.l

2

"~

Table 87 Spark Gaps for Air at 760 mm Hg (in mm)

~

Form of ~. ~clectrodes Potenti ill _______________

di fference, v

_______________

20,000 40.000 !OO,1I01l 2110,000 301l,OIJO

, II-Ip~;;::: ~jJ-llfjJe

~

TO/(

Two

Two spheres

\,oi Iltcd

of di<.ll1lciL'r

wires

1 S. 5

,I;) . .5

5

('Ill

;).

41

1J 4S 2li2

GOO

530

Two plates

G.1 1:l. 7

3G.7 75.3 It4

~

"<:::~

"\ ".~ t\. "\ ~ ~

Fig'. 48. De. pendence of resistivity of germani um (10·

/I-Ip)/~~~ 0-

'P-I)jJ~ '\ ~

,

"::: 10

]e

02

10."

1It/lllbor OI/1l7;Jl/l'Ily

I(J

'I.

10

010117$ jJl?r CIlI J

"

~" ~

wer curves) and 5i Ii con (upper Curves) 011 concen tra. Ii on of i m purl ty atoms. Tempe'rat ure--aboul 20°C.

~

ELECTROMAGNETISM

FUNDAMENTAL CONCEPTS AND LAWS

1. The Magnetic Field. Magnetic Induction If a freely pivoted magnetic needle is placed near a wire carrying current, the needle will be deflected (will Le oriented in a certain direction). The forces causing this deflection are called magnetic forces.

CP. IV. ELECTRICITY

132

FUNDAMENTAL CONCEPTS AND LAWS

A region of space in which magnetic forces act is called

a magnetic field. . A magnetic J1eld docs not act upon electric charges at res t. The direC"iiol1 of the magnelic field is defined as the dire~­ tion of the force actin;:; on the north pole of a magnetic needle placed at the given point of the field. The force act ing on a wire carrying current in a magnetic field is determined by Ampere's law: F = ilB sin ~,

(4,45)

where I is the 1cn,~th of the wire, ~ - the angle between the direction of the magnetic fie Id and the current in the wire; i, and 13 are expressed in the same system of units. The quantity in equation (4,45) characterises the magnitude and direction of the magnetic field and is called the magnetic induction. The magnetic induction is numerically equal to the force which the fnagnclic field exerts up'in unit length of a straight wire carryin7, unit current when the wire is perpendicular to t he field. The li1agnetic induction is a vector quantity. Its direction coincides with the direction of the magnetic field. The magnetic induction depends on the properties of the medium. The magnetic field surrounding a current-carrying wire can also be characterised by another quantity, called the field intensitl! (Ii). The field intensity i" independent of the properties of the medium; it is determined by' the current and the shape of the conductor. . B The quanhty l-"=H charac-

n

Fi~.

;;u. LcH-.!land rule.

terises the magnetic properties of the medium and is called the permeability ot the medium. The direction of the force acting on a current-carrying conductor is determined by means of the left-hand rule: if the open palm at the left hand is placed so that the lines of force of the magnetic field enter the palm, while the outstretched

133

fingers point in the direction of the current, then the thumb will indicate the direction of the force actin:.; on the conductor (Fig. 50). Two sufficiently long straight parallel conductors of the same length I carrying currents i, and i 2 , respectively, interact with a force F -

-

2ftiJ2 1 a '

(4,46)

where a is the distance hetween the conductors and It is the permeabi Ii ty of the medi Lim. Currents flowing in the same direction attract, currents flowing in opposite directions repel each other. The force acting on a moving charge in a magnetic Held (called Lorentz' force) is

(4,4.7) where e is the charge, v-the velocity and a-the angle between the direction of the velocitv and the indtlction 13.1 he Lorentz force is directed perpend(cu lar to the p lane determined by the vectors B and v. 2. CGSM and 1VI/(5A Systems cf Units In the CGS electromagnetic (CGSM) system t:Je fundamental units are the centimetre, [f,mm (mass), second, and for electric quantities -- the pl'rmeal:ility. The permeability of vacLium (flo = I) is taken as the l111it of permeability. The unit of current in this system is derived [rom the law of interaction of currents (4,46). The unit of curren tin the CGS,'Vl svs tern is defined as such a direct current which, when fJo\\'in~g throl.gh t\\'o infinitely long parallel wires placed in vacuum I cm apart, causes them to interact with a force of 2 dynes per em of their length. It is assumed that both \1 ires have a sufficiently small cross-sectional area. The fundamental units of the MKSA svste!l~ are the meter, kilowam (mass), second and the unit o'r current ---a:ilpere. An ampere j,; defined as sl!ch a direct cllrJl'nt wllich when flOWing tlIrollgh two inl1nitely IOllg pilralil'l wires placed in vacuum at a distance of one meier caLl:"~, thelll to Interact with a force of 2X 10- 7 M.l\SA units of force per meter of their length.

135

CH. IV. ELECTR ICfTY

FUNDAMEJ\TAL CONCEPTS AND LAWS

In this system the permeability is a derived quantity. For vacuum fto= 10- 7 henry/meter.

by an element of conductor of length I1l carrying a current i is (Flg. 53) !J.H_i!J.1 sin a (4,48)

134

The unit of magnetic field intensity in the CGSl\1. system is the oersted; in the 1'v1KSA system - the ampere per meter, (amp/m). An oersted is defined as the intensity of a magnetic field which acts on 1 cm of a straight conductor carrying 1 CGSM unit of current with a force of 1 dyne. 1 amp/m = 10- 3 oersted. The unit of magnetic induction in the CGSl\1. svstem is the

gauss; in the MKSA system - the u.'eber per square meter (weber/ m 2). 3. I ntensity of the Magnetic Fields of Currents The lines of force of a magnetic field are defined as curves, the iangents to which coincide in directlon with the intensity at each point. The ma~netic lines of force are closed curves (as distinct from the lines of force of an electrostatic field); such fields are called vortical iields. The lines of force of a straight currentcarrying conductor are concentric circles lying in a p lane perpendicular to the current (Fig. 51). The direction of the magnetic Fig. 51. Magneli c Ii nes of force of a line" of force is determined straig-ht \Vi re carrying current, pat~ by the right -hand rule. tern formed by iron fili ngs. If the thumb of the right hand is p laced a long the wire pointing in the direclion of the current, the curled fingers of the right hand will point in the direction of the magnetic lines of force. (Figs. 51, 52 and 53). Fig. 52. fr\:\gnctic field flue to curThe intensity of the rent in a solenoid, pattern formed magnetic field generated by iron Ii lings,

-

,2

,

where r is the distance from the eleme,;.t !J.I to the point for which the intensity is sought, a - the angle between !J.I and r. This relation is called Biot and Savart's law. The magnetic field intensity of a long straight currentcarrying wire is H=2i, a

Q (44 ' ~)

where a is the distance from the wire to the point at which the intensity is sought. The magnetic field intensity at the centre of a circu lar loop of current-carrying wire is

H =2Jti ,

R

(4,50) Fig.

53.

Illustration

of

Biot and Savart's law. where R is the radius of the loop. The magnetic field intensity inside a toroid (Fig. 54) is

H -

2Ni r '

(4,51)

where N is the total number of turns of wire, r - the radius of the toroid. The field intensity inside a straight solenoid, whose length considerab Iy exceeds the diameter of a turn is

If=4Jtlli,

(4,52)

where n is the number of turns per cm of the length of the solenoid. In such a solenoid the field intensity is the same in magnitude and direction at all points, i.e" the field is homogeneous.

CH. IV. ELECTEIClTY

FUNDAMENTAL CONCEPTS AND LAWS

In electrical engineering the product ni for a solenoid is called the number'of ampere-turns per centimeter. . I oersted = I}GAn ampere-turns}cm = I ar!lpere-t.ur~/CtJ?' The field intensity of a moving charged particle (FIg 05) IS

The uni.t of magnetic flux in the CGSM system is the maxwell, 111 the MKSA system - the weber \Vh~n the ma~n~tic fl L1X through a circ~it is changed an ~leetf1c current IS mduced !ll the curcuit. This phenomenon IS called. electromagnetic induction, and the current thus genera ted IS called an induced current.

136

(4,53) where v is the

velocity of the

137

particle, r -'- the distance

Fig. 56. Magr.letic flux through surf
Fig. 54. Toroi d.

Fig.

field of moving cllargc.

,'J:-). I\\agrldi:

from the particle to the pnint of interest, {f - the anEOe between the direction of the velocity ,111d the line drawn tram the particle to the gi ven point of the fIeld.

4 Work Performed in the Motion of a Current· Carrying . Wire in a Magnetic field. Electromagnetic Induction When a current-carrying wire moves through a magnetic field work is performed: A = i (tD 2 - tD.), (4,54) where !D is the magnetic fiux through the current lo?p prior to "displacement and !D2 - ti1e ma:~nehc flux after dISplacement. . The magnetic flux through a loop ('n a homogeneous field) is defined as the prodUct of the magnetic induction by the area of the loop and the cosine of the angle behveen the direction of the field and the normal to the area of the loop (Fig. 56) (4.55) !D := 13& cos a.

The direc.tio~ ,of the induced current i,; alway,; ,uch that the magnetIc flej(l of the current opposes the chiJIwe jl] fluX which camed the induced curren' (Lenz' law). c-.· [he magnItude of the Induced electromotive force is g;ven by the formula

!'ltD g;=--. At

(4,56)

In other words, the induced e.m.!. is equal to the time rate o.f change .of ~he magneti~ flux through the loop. The nega' lIye slgnwdlcates the c1neetlOll of the e.m.!. (in accGrdance WIth Lenz' law).

5. Self-Induction Any change in the current in a conduetor lead' to the appearance ~:r a'1 Indl,cecl e.m.f., which ca,lse:; a current llJ~' rement. ] [;1'; phenumenon is cailed .Iel f- illduction. [he ,elf-lli'lUCcd c.m f. CQ/J be cumputed by the fornw!a:

l£s=-- 1 ~ - 6.t '

(4,57)

138

CH. IV. ELECTRICITY

where L is the self-inductance,

~: -

FUNDAMENTAL CONCEPTS AND LAWS

the mean rate of change

of the current in the time interval !1t. L depends on the geometrical shape and dimensions of the conductor and on the properties of the medium. The unit of inductance in the MKSA system is the henry, in the CGSM system - the centimeter. A henry is clefined as the inductance of a conductor in which a change of current of 1 ampere per second induces an c.m.I. of 1 volt,

The region of space in which a magnetic field exists contains stored energy. The energy density of a homogeneous magnetic field (the energy per unit volume) can be computed by the formula: ft

H2 *

W=--

8rt

•

(4,63)

The inductance of a solenoid v,;ith a core is (4,58) where [I is the permeability, S - the cross-~'ectional area of the solenoid, 1- the ]en[~th of the wire, k - a coefficient depending on the ratio of the length of the wire to the diameter of the coil (lid). Table 96 gives values of k. It should be observed that when L is computed Using formula (4,58), the quantity ft for ferromagnetic materials will depend on the shape of the core. The inductance of a coaxial cable of length I is

~~ ,

(4,59)

where R2 and R 1 are the radii of the external and internal cylinders. The inductance of a two-wire line of length I and radius of the wires r (for r ~ a) is

a L=4ftlln - , r

(4,60)

where S is the cross-sectional area of the pole-piece of the magnet, and ftll - the permeability of air. Eddy carrents are induced currents in massive conductors placed in a variable magnetic field.

6. Magnetic Properties of Matter

Magnetic materials are materials in which a state of magne!isa!ion can be induced. When such materials are magnetised they create a magnetic lield in the surrounding space. The degree of magnetisa!ion of a magnetic material is characterised by the magneti,rztion vectO" I which is proportional to the field intensity generateel by the material. The magnetic inductiun Ii is a vector quantity which is equal to the average value of the induction inside the material. This quantity is composcd of the induction due to the field of the magnetising current (~L"H) and the induction due to the Held of the magnciic materi al (4;t/): (4,64) where fto is the permeability of vacuum. The magnetisation vector and the intensity of the magne!ising field are connected by the formula:

I=XH, where a is the distance between the axes of the wires. The energy of the ma:.;netic field of a conductor carrying current is

w=J.. Li2. 2

(4,62)

The lifting power of an electromagnet is given by

1 henry=lG 9 em.

L=2,lllln

139

(4,61)

(4,65)

where the quantity X, called the magnetic susceptibility, depends on the nature of the magnetic material and 011 its state (temperature, etc.). ~

See footnote on p. 99.

140

CH. IV. ELIi:CTRICITY

Since B=ltH, then

TABLES AND GRAPHS

+

/-t=/-to 41tX. (4,66) Materials for which /-t> 1 (but smal!!) are called paramagnet ic; if /-t< 1 the material is called diamagnetic. Materials for which /-t is much greater than unity are called ferromagnet ic. Ferromagnetic materi a Is are crysta Iline. Ferromagnetic and paramagnetic materials differ in a number of thei I' properties. a) The magnet isation curve, which expresses the relation between Hand B, is a straight line for paramagnetic materials, but it is an intricate curve for ferromagnetic materials. This means that /-t is a constant for paramagnetic materials, while for ferromagnetic materials it depends on the field intensity. b) The magnetic susceptibility of ferromagnetic materials varies with the temperature in a more complicated manner; at a certain temperature Tc called the Curie temperature (Cur ie point) the ferromagnetic properties disappear: the ferromagnetic substance becomes paramagnetic. . c) The magnetisation of a ferromagnetic material depends. !Il addition to the field intensity, on the magnetic history fa the sample: the value of the induction lags behind that of

a

J 41

The coercive force (H r) is the value of the magnetic field intensity needed to reduce the residual induction to zero (the direction of this field must be opposite to that of the retentiVity). . The saturation value (Is) is the greatest value of the magnetisation I. When a ferromagnetic material has been magnetised to the saturation value, further increase of the field intensity will have practically no effect on the magnetisation. The magnetic saturation is measured in gausses. The initial permeability (/-to) is the limiting value of the permeabi lity, when the intensity and the induction tend to zero, I.e.,

/-to= lim /-t. H

->0

The properties of ferromagnetic materials are explained by means of the domain theory of magnetisation. According to this theory, in the absence of an external magnetic field a ferromagnetic material is composed of many small regions or domains each magnetised to saturation. In the absence of 2n external field the directions of magnetisation of these domains are distributed in such a way that the total magnetisation of the specimen is zero. When a ferromagnetic material is placed in a magnetic field the domain boundaries are displaced (in weak fields) and the direction of magnetisation of the domains rotates towards the direction of the magnetising field, a. a result of which the material becomes magnetised.

ft.

TABLES AND GRAPHS Magnetic Field of the Earth Fig. curve

57. of

Hysteresis

100P:Ol-

magneU sati on

from

unmagnctised state. 123-demagnetisati on curve.

the field intensity. This phenumenon is called hysteresis and the curve ,Iepicting the depel1dence of B on H in the p;ocess of remagnetisalion (fIg. fi/) is called a hysteri'ois loop The nlue 01 the lesldllal magnetic induction IIf the ferromagnetic materi al aftel' the magl1etising field has been reduced to zero (H=O) is called the relentivity (B ).

r

The earth is surrounded by a magnetic field, The curve drawn through the points of the earth's surface at which the intensity is directed hori zan tally is called the magnetic equator. The points of the earth at which the intensity is directed vertically are called the magnetic poles. There are two such points: the north magnetic pole (i n the southern hernispl1erC) and the south magnetic pole (i n the northern hemisphere). The magnetic field intensity at the magneti c equa tor is about 0,34 oersted; at the magnetic poles it is about 0.66 oersted. In some places (the regions of the so called magnetic anomali es) the i lItensity increases sharply. In the region of the K.ursk magnetic anomaly it is 2 oersteds.

142

CH. IV. ELI'!CTRlCI1"Y

143

TABLES AND GRAPHS

Table 90

Table 88 Properties of Some Steels Used in Electrical Engineering

Steel

Initial permeability. 'gauss,ocr·

sted 250 300 400 GO 0 1,000

'" 31 '" 41

'" 42 '" 45 '" 310

!Y1axi1l1ut11 permeability, gauss oersted

Cocrci ve force, oersted

5,500 0,000 7,500 10,000 30.000

0.55 0.45 0.4 0.25 0.12

IInduction at 25 oerI

steds, ~ra uss

15,200 14,900 14,'100 14, GOO 17,800

Properties of Some Magnetically Refractive Materials These materials ~lfC c1Jaracteri~cd hy <:1 high coerci ve force, :lnd are used in the lnanufactufc of permanent magnets. The maximum

Eleelri c resi sti vi ty. ohm

value of the quantitv HB is an Important characteristic. -

8",

tity is proportional to the maximum energy of the surroundi ng the ferromagnetic rna teri a1.

mm 21 m

This quan-

magnetic field

1\'\J.xi111um

0.52 0.0 0.0 0.02 0.5

Coercive Magnet materi al

Rctcnti~

force,

viiy, gauss

oersted

Alioys: alni alnico <:dnisi magnico . . Chromium s(Pel 9F X3i\ Cohalt stecl ,)F 1<:30 . Molvbdenum steel . . PlatinulTl alloys . . . Tungsten steei 9FBA

s,son

IDO,OOO 11,000 37,000

In.ono -1,5006,800 10,000

Table 89

12.000

2:'()

liO

52,000 G1,000

7,()!I() 4 , () Oil J 2 ,() 00 [I,O()O ~I , 000

It

65 1 ,500-~, 700

value of quantity lIB'8"" erg/em:1

5G,OOO

Properties of Some Iron-Nickel Alloys These alloys have a high rermcabi lity, which decreases sharply at high Ii cld intensi ti es and hi gh frequenc ies. a nd in addi ti on, depends strongly 011 mcclElni (';}! str<1i ns.

Alloy

Chromi um-permailoy (HBOXC) Giperonl :J 0 Giperom 766 . . . . . iron, icchni cally rJtHC Molybden um-permal· loy (4% Mo) . Permcndur Sili can iron Superperrn al ioy (5% \ Mo)

Ini tial pcrrncalJilily, gauss ocrsted

l\laximum

3,000 3,400 14,000 200

Isn,OOO

2,000 800 4 C, 0

i 20, O()O A ,;) ()() 8,000

pcrmc<:llJi -

lily, gauss

,,8,O(}O '15,0 ()() 5,000

__ __sno,ooo

100.000 .

.

..

Table 51 Cocrcive force. oer.stcd

SatufJtion value of maf:!'net isation, gauss

0.015

6,500

0.0·\ 1.0

21,500

0.02 2.0 0.4-0. G

8,500 21.000 20,000

o .(I(i

0.0:11

7,500

,

Properties of Magneto-Dielectrics Magneto·dielectrics (and ferriles) are materials possessing both a relatively high magnetic permeability and a high electric resistivity,

Material

Alsifer pq·6 . pq·9 . <.1>11 25 Carbonvl iron Magneli te

[1.,

lvlC1ximum ope·

5-G 9-10 20-2·[ II G-D

tiD 2-3 I 30·50 5·10

g-auss'ocrsted [ rati ng frequency. l\1c;sec

145

TABLES AND GRAPHS

CH. IV. ELECTRICITY

144

Table 94

Table <;2 Principal Properties o[ Ferrites

Curie Points of Metals

Ferrites are mixtures 0\ metals (nickel, zinc. iron) sn1Jjecled to special heat treatment, as a result of which they acquire a high reo sistivity.

Substance 1'-, gauss/oersted

Ferri te

liOO f)GO

55 711 1111 120 LliJl

400 200 200 1511 15 10

1"1I 1211 250 360 400 400

2,000 2,000 1,000

Ferrocart-2 , 000-1 Ferrocart-2, 000-1 I Ferrocart-I ,000 Ferrocart-600 Ferrocart-500 Ferrocart-400 Ferroeart-200 Ferrocart 11-4 Ferroeart H-5 Ferrocart P4 -15 Ferracar t P4 -10

M(lximum opera li ng temperature, °C

B max' gauss

2,500 2,500 3,200 3, I 00 2,800 2, ;,00 1,800 4,200 4,800 1,8S0 1,400

Gadolinium Permalloy, 30% HellS ler alloy Nickel . . . . . Permalloy. 78%

I

Te, °C

20 70 200 35 R 550

I

Substance

Te , °C

Magnetite... . Iron, electrolytic Iron, resmelted In hydrogen Cobalt

585 769 774 1,140

Table 95 Specific Magnetic Susceptibility (per gram) of Some Metals at 18° C in CGSM Units

Table 93 Permeability (~t) of Paramagr.etic and Diamagnetic Materials in CGSM Units

The specific susceptibility 'sp is eqllal to the ratio o[ the susceptibility

x

to the density o[ the material p: 'sp=.x.. .

:'

Metal Paramagnetic \ _ _m_a_te_r_ia_l_ _-'-_(I_'_-_I_)_X_l_O_;,;-

Air . . . • . • Aluminil.lm Eboni te Li qui d oxygen Ni trogen . Oxygen. Platinum Tungsten.

0.38 23 14

3,400 0.013 1.9

3GO 176

Diamagnetic m_a_t_e_l"l_·'_11

Benzene Bismuth Copper . Glass . . Hydrogen Quartz . Rock salt . Water . . .

\ 1 ( -

'sp X 10'

Metal

'sp X 10'

10' p.) X

7.5 17G 10.3 12.6 0.063 15. I 12.G 9.0

Aluminium Antimony Cadmium. Calci um Chromium

Copper Germani lllll Indium. Lead . . Lithium

0.58 -0.87 -0.18 0.5 3 6 -0:086 -0,12 -0.11

-0.12 1I.5

/vlanganese /Vlerc-ufY

.

Scleni um .

511ver Sadi urn Tclluriurn Tin. . Tungsten . Vanadi urn Zinc

7.5 -0.19 -0.32 -0.20

o

G

-0' 31 0.,\

0.28 1.4 -0.157

--_._----=-------_._-_--!...---10

").1J'.

16

CH. IV. ELECTRICITY

146

FUNDAMENTAL CONCEPTS AND LAWS

Dependence of Magnetic Permeability and Induction on the Magnetic Field Intensity /! 10000 ?DilDO

I I I -\ I I

II

10000 ,

Ratio of length of to di ameter (if d)

/

.L. l/?~

If; \,/:f

15000

Permo//a>,

i\ 50000 0

10000

1\ 1><1-.; Ar!1lCo/rOll

1/

~ O.l

SOJO

I I 0.9

o.p

0.8

1/ o

H,oers/e&

I---

V

20

40

- -

00

SO

100

13,91111SStS

J\l iTOn_ Sw

/BOOO

,,-

/2000 8000

-

10-

V

1/

~

/

~ ~

~~ -

fOO0

'-120

~

-80

40

40

80

-'

120

Il,0ers!etl$

II

-8000

k

r--

/20

Note.

For

lrd~

lO" is dose to

llnit~y.

H,oers/e{$

Fig. 5~)' Dependence of i ndllC~i,().n o~ intensity (curve]- electrolytic tron, curve 2 - Iow- carbon steel,. curve 3 - cast steel; curve 4 - cast !fan).

Fig. 58. Dependence of permea· bility of iron and permalloy all the intensity in weak helds.

D. ALTERNATING CURRENTS FUNDAMENTAL CONCEPTS AND LAWS An alternating current is one which periodically reverse,; its direction. A current which varies periodically only in magnitude is called a pulsating direct current. In practice most frequent use is made of alternating currents which vary sinusoidally (Fig. 61). Periodic currents which vary otherwise than sinusoidally can be repre',ented to any degree of approximation E by a sU1110f sinusoidal alternatim; currents (see p. 77). The instantaneous values of a sinusoidal alternating current and voltage are given by the formulas: t i=! m sin wt, (4,67) u=U m sin (wt qJ), (4,68)

+

w=2rtf,

1/

"12000

V

-1600.'U

I ... j:::"

l-- ~ './

Fig. 60. Hysteresis loop for soft irull Jlld tempered steel.

\

Ta/)Ie 96 Values of Coefficient k for Calculating Inductance

B.iflPSSP!

;COOO

147

(4,69)

where! m and U m are the maximum values (amplitudes) of the current and the voltage, w is the ?=O). angular (cyclic) frequency of the current, t - the time, qJ - the phase shift between the current and the voltage (see p. 76), f - the frequency of the current. 10* Fig. G 1. Graph of alternati ng e.m.f. and current (sine law,

148

149

TABLES AND GRAPHS

CH. IV. ELECTRICITY

The rfJcctive value of an alternating current (1) is defined as the direct current which would develop the same power in an active resistance as the given alternating current. In most cases (but not always!) ammeters and voltmeters show the effective values of the current or voltage. For sinusoidal currents

For Rr=R c the impedance is a minimum (see formula (4,74», a~d the current has its maximum value. This phenomenon IS called series resonance. The phase difference between the current and the voltage is determined fl'om the relations:

t an qJ

wL-~ wC R

(4,70) cos qJ=

}

'

(4,75)

i.

(4,71) The power developed by an alternating current in the circuit is An inductor L (a device possessing inductance) in an alternating-current circuit acts like a resistance RL in the circui t, 1. e., it red uces the current. The quantity RL which describes the behavior of an inductor is called the induct ive reactance: (4,72) and is due to the appearance of an e.mJ. of self-induction in the coi 1. An alternating current in an inductor lags behind the voltage by 90 0 • A capacitor in an alternating-current circuit conducts current (as distinct from direct current!). The quantity which describes the behavior of a capacitor in an alternating-current circuit is called the capacitive reactance:

I

Rc=wC'

P=UI cos qJ.

The factor cos qJ is called the pOiL'llr factor. . When an ~lternating current passes through a conductor It,generates mduced currents; as a result the current density wI.ll be greater. at the surface of the conductor than in the rmddle. The dlff~rence will b.e the greater, the greater the frequency (at high frequencies the current in the middle of the conductor may be practically zero), The active resis~ance of a conductor will therefore be greater to alternat1I1g current, than to direct current. This phenomenon is called the surface effect (or skin eOect).

TABLES AND GRAPHS (4,73)

The current in a capaci tor leads the voltage by 90°. In a circuit containing resistance, inductive reactance and capacitive reactance connected in series the quantity

Change in Resistance upon Transition from Direct to Alternating Current The change in resistance depends on a parameter ;: t=0.14

(4,74) ca \led the impedance, is analogous to the resistance of a direct-current circuit.

\

(1,76)

d~VI

p.! p

,

where d -!s ~h~ diameter ot the wire (cm), f - the frequency (clsec) c. the resl stl VI ty (ohm cm). fJ. - tlle permeabi Ii (Y. R·,c -- t he resis~ tance the wi.re to atternating current, Rdc - the rcsi;tance 01 the same WIre to dIrect current.

0:

FUNDAMENTAL

CH. IV. ELECTRICITY

150

CONCEPT~ AND

LAWS

j/ue.

Table 97

lilTC 7

lSI

f-- 1--

Derlh of Penetration (a) of High frequency Currents (for a Straight Copper Wire with Circular Cross-Section)

. . . ., v

6

V

5

./ /'

4 3

j,/"

Frequency

Dept h of pene· tration. mm

2

V o

Z

4

6

8

/0

IZ

t=D,!4d~ '.,2. Graph of

Fig.

14

/0

18

to i

0=50.33

1/00

.

,

$00

700 C)

~ <S

600

~

500

~ .~ 400

1\\

"'" 300 ~O0

JOO

t'~

1\ 1\

i//

z\ 1\ \ \

V 1/ \ 1/

K .\ . a ~t1 Jl

I

/QOP

500'

t}ciic (refjllellCf, (rQ'ftilllls/seC) l
L

, R

L=l licnry. C=IO p.fd.

c'

0.006

-{p~

.

where p is the resistivity (ohm mm'!m). I'- - the permeability of the malerial, f - the frequency (c. sec). 2. The dcpth of penetration is the distance from the surface of the wire at which the current density is e times less than at the surface. where e is the base of natural logarithms Ie"" 2.72).

fUNDAMENTAL COI':CEPTS AND LAWS

/

tuNS

0.021

E. ELECTRIC OSCILLATIONS AND ELECTROMAGNETIC WAVES

V /z

/

O.OG5

/

VV

V'......

Me'sec \10 MC'seC/IOO MC,'sec

'~z

",~V

\\

0.21

Rac/Rdc

\ariation of In([uct;ve Reactance,. Capacitive Reactance and Impedance with frequency

tOOO

O.G5

II

Notes. I. Calculations can be made for other frequencies and other materials by means of the formula

Versus ;.

.sOO

\ 10 kC!SCCllOO kcisec

V

and Z versus

It)

for

Ra=IOO ohms (it is as-

sumed that R a is independent of the frequency).

Osci lIatory variations of the charge, current or voltage in an electric circuit are called electric oscillations. An alternating electric current is an example of electric oscillations. High·frequency electric oscillations are generated as a rule by means of an oscillating circuit. An oscillating circuit is a closed circuit containing inductance Land capaci tance C. The period ot natural oscillations of a circuit is (4,77)

FUNDAMENTAL CONCEPTS AND LAWS

CH. IV. ELECTRICITY

152

153

Electromagnetic waves represent a process of simultaneous propagation of variations of electric and magnetic fields. The vectors of the electric and magnetic field intensities (E and H) in an electromagnetic wave are perpendicular to

!

t

E

Fig. 64. Graph of current in circuit with damped ooci !lations.

This relation is called Thomson's formula; it is valid in the abspnce of energy losses. In the case of energy losses in the circuit (when an oh1m mic resistance is present) the natural oscillations of the circuit are damped:

T

2Jt

-./~

V

_(ll)2' (4,78)

LC

The term

2L

UR

is

usualIy

very small. Fig. 64 represents l.-.----.L11 a graph of damped asci llaYres tions in a circui t. When an alternatinge.m.f. Fig. 6;). l
Fig. 66. Vectors F. H, ond netic wave.

,J

in eleetrot11a:;-

each other and to the direction of propagation of the \\'JH'S (Fig. 66). This is true for the propagation of e!cdroma;;nctic waves in vacuum. The velocity of electromagnetic waves in \'acuum is independent of the wavelength and equals

co=(2.99776 ='= 0.00004) X 10 '0 em/sec. The velocity of electromagnctic \Vans in diITcrcnt media is less than in vacuum:

c,

C=n'

(4,7J)

where n is the index of refraction (sec p. 15e:). The Electromagnetic Spectrum The wavelengths are plotted logarithmically, The fir~t horizontal row gives the wavelengths (upper values III dIfferent nni ts of length, lower values in em). The second row gives the frequencies in eycles'sec, the third and fourth rows - the names of the wavelength and frequency ranf~es. I~ows 5 and 6 show the types of electromagnetic radiators rOIlS 7 ami 8 --- the principal methods of generatin Cf electro: lIlagneiic oscillaiiol1s. "

...'" (conI:)

10 8.km

'. 00==;c

_

1O",km.

/! I.,~.I/o"! ,-"-' , I! ~J ISI,n;!" J

r

1;,08

II

I

3'10"

II

I

tow fTey'ue11iies

Au{/;o

.2-.L

n

,f'(J(//O wupes

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156

CH. IV. ELECTRICITY

Low-frequency and radio waves have the lowest frequencies; such waves are generated by various artificia I osci lIa· tors. Infrared radiation is emitted mainly by oscillating parts of molecules or groups of atoms. Light waves are emitted by atoms and molecules when electrons in the outer shell pass from one stable orbit to another (see p. 188)_ Ultraviolet rays have the same origin as light waves. X -rays are emitted when electrons in the inner shells of atoms pass from one orbit to another. Gamma-rays are emitted in the radioactive decay of atomic nuclei. Further information on the properties of various types of waves will be found in Chapter V; Optics.

CHAPTER V

OPTICS FUN DAMENTAL CONCEPTS AND LAWS Light is electromagnetic radiation of wavelength considerably shorter than that of radio waves (see the electromagnetic spectrum). Such radiation is emitted by atoms when their electrons jump from one orbit to another (see p. 188). 1. Photometry The energy radiated by a body per second is called the intensity of radiation. The energy transmitted by a light wave per second to a surface is called the flux of radiation through the surface
where
IS8

CH. V. OPTICS

FUNDAMENTAL CONCEPTS AND LAWS

The unit of luminous flux is the lumen. One lumen is equal to the luminous flux contilined in a solid angle of one steradian when the luminous intf'll:ii ty is one candela. Prior to the introduction of the new standard candela. the international candle in the form of electric hulbs of spe~ cial design was used as the standard of luminous intensity. I internationill candle=1.005 cande las. 0:.. The illuminance (E) is the luminous flex incident on unit area of a surface:

2. Principal Laws of Geometrical Optics

.::t>IB}~~!ilEt2]__ 2

'.:.

3

5

E=S' cD

(5,2)

\\here S is the surface area receiving the luminous flux. The units of illuminance are the lux and the phot: I lux=1 lumenjm 2 , I phot=1 lumen j cm 2 •

Fig. G8.

liSSR Slale standard light source: 1 - platinum. 2 -fused tho.rium oxide tube. 3 -fused thorium oxide cup. 4 - thorium oxide powder, 5 - silica container.

The brightness of an extended l',h1 source (or surface seen by reiJected light) is referred to technically as its luminance (B): J

B=5'

(5,3) ..

where S is the visible area of the surface (the area of the projection of the surface on to a plane perpendicular to the line of vision), and J is the luminous intensity. Luminance is expressed in units of luminous intensity per unit area, as cande las, m 2 • An old unit of luminance is the stilb. A stilb is equal to the luminance of a source which radiates a luminous intensity of I candela per em" of luminous surface. 1 stilb=lO' candelasJm 2 • Photometry deals with luminous intensity, luminance and iJlumimnce, as determined by visual perception and from measurements of the luminous llux.

159

Geometrical optics deals with thosc phenomena which can be explained on the assumption thilt \j';ht travels through a homogeneous medium in a strai~ht line. The angle of incidenc~ is the angle between the incident ray and the normal to the interface between two media at the point of incidence. The angle of reflection is the angle between this normal and the reflected ray. The angle of refraction is the angle between the normal and the refrilcted ray. I. When a ray is incident on the interfilce between two media the angle' of incidence is equal t~ the angle of reflection. The incident ray, the normal, and the reflected ray all lie in the same plilne. The magnitude of reflection is characterised hy the reflection coefficient p, which is equal to the ratio of the energy flux in the reflected wave to that in the incident wave. (The reflection c02fflcient is frequently expressed in per cent.) 2. The ratio of the sine of the angle of incidence to the sine of the am,le of refraction is a constant (for a gi\'en wavelength). The incident ray, the normal, and the refracted ray are in the same plane. sin i

-.--.,=n. SIll I

(5,4)

The quantity n is called the relative index of refraction of the second medium with respect to the first medium. and is equal to the ratio of the velocities of light in the two media: n=S- .

c,

The inde£ of refraction with respect to vacuum is called the absolute index of refraction of the medium. The index of refraction n depends on the wave length. A ray passing from a medium with a greater index of refraction to a medium with a smaller index of refraction can undergo total reflection. The least angle of incidence i er at which all the energy of the light is reflected from the interface is called the critical angle. The magnitude of the critical angle i er is determined from the formula ..

I

SIll1er=n'

CH. V. OPTICS

160

161

FUNDAMENTAL CONCEPTS AND LAWS

where n is the relative index of refraction of the medium in which total reflection takes place. Rough surfaces reflect light rays in all directions (di[fuse reflection), as a result of which they are visible to the eye. When light passes through thin metal plates its intemity is reduced. The change in the luminous intensity (for nor· mal incidence on the plate) is given by the relation -

/ x=/oe

4~n :::- k I.

Fig.

0~.

Path of rays io thin cOllvcrging lens.

where /0 is the incident light intensity, / x - the inte nsity of the light after passage through a plate of thickness x, A - the wavelength, e ~ the base of natural logarithms. n and k - optical constants of the metal which are determined from the relations

n 2 k= ~ , n 2 (1 - k 2 )=e. Here a is the conductivity of the metal, v - the frequ"nc' of the light wave, and e - the dielectric constant. 3. Optical Instruments The formula of a thin lens (Fig. 69) is

-~+J,=(n--I)(~-~i=~, a a r r ) f l

(5,5).

2

where a is the distance from the lens to the object, a'the distance from the lens to the image, f - the focal length of the lens, r l and r2 - the radii of curvature of the spherical surfaces of the lens, n - the relative refractive index of the material of the lens. In formula (5,5) the quantities a, d, r l , and r 2 are considered positive when their directions, as measured from the lens, coincide with the direction of the light rays; otherwise they are considered negative. The magnification of a magnifying glass is

M=250

f ' where

f

i~

the focal length in mi Iii meters.

Fig. 70. Path oi lent to microscope to optical system

cro'Co'H'. 0

1

( ) ! - krhe''' '''1 1I iva.. 0: --- lens cqU\ v:d~nt i l1lJge 01 . .-'dJ ull reU na

.1nd

L'yepi l'CC.

/1. 2 Liz, -

eye.

l,

(5,6) Fig. 71. PaUl 01 ray,-'; III tc1cscop-:. I - r;ly:; l·lllL~rgi jIg from a single point of the object. :2 - rays emcrgi llg troiU
-

-

-

__

n

_

CH. V. OPTICS

162

FUNDAMENTAL CONCEPTS AND LAWS

The overall magnification of a microscope is

M --~t1 X 250 t2

'

(5,7)

where t1 and t2 are the focal lengths of the objective and the eyepiece in millimeters, ~ is the distance from th~ upp~r focus of the objective to the lower focus of the eyepiece In millimeters (Fig 70). The magnification of a telescope is

M=0, t2

(5,8)

where tl and 12 are the focal lengths of the objective and the eyepiece (Fig. 7i). The reciprocal of the focal length is called the power of the lens: D=+. The unit of pO\ler of a lens is the diop.

ter (D), equal to the of I m.

PO\\

cr of a

lens \\ith a focal length

4. Wave Prcperties of Light Interference. When two waves travel simultaneouslY through a medium there will be a resultant vibration of the particles of the medium at edeh point (in the case of mechanical waves), or a resultant oscillation of the electric and magnetic field intensities (in the case of electr0magnetic waves). The resultant 0scillations will be determined by the amplitude and tlie pl,ase uf each of the waves. The superposition in space of two (or more) waves of the same period leading to a reinforcement of the resultant amplitude at some points and to a diminution of the ampli tude at others is ca lied interterence. Interference of waves of any kind (including light waves) takes place only if the superposed waves have the same period and a constant phase difference at each point. Sources which generate such waves are called coherent. For polarised waves (see p. 166) to di5play interferen.ce it isnecessary in addition, that their planes of polansatlOn ~ol~clde. Coherent sources of lif:ht can only be obtall1ed artIfiCially. In a homogeneous medium every colour corresponds to a definite frequency "f the w'lve. When a wave passes lI1to another mediU1l1, the w;;"elength changes, but the frequency remains the same.

163

Daylight consists of electromagnetic radi:dion of various wavelengths (corresponding to colours from red to violet). 1 he colours of thin films arc due to the interference of w~ves reflected from the upper and lo,ver surfaces of the film (when observed in reflecteJ light). When observed in transmi tted ligh t in terference takes place between the trans· mitted w~ves and the waves refiected from the upper ::nd lower surfaces of the HIm. Diffraction. The defleclion of light from a rectilinear path otherwise than by rellection or refraction is called diflraction. Fig. 72 depicts schematically a lon~ narrow slit, by me:ms of which it is possible to observe the phe. nomenon of diffraction. Light falls perpendicularly on the ;urface containin,!': the sli!. Upon passing through the ;lit the jif(ht rays 3re deflect2d from a' strail(11t path, and as a result of the sLibsequent superposition (interference) _ _ _-:I,;., of the ligh t waves one wi 11 observe light and dark fringes Fig. 72. Dilfradion of pare_dIel on the screen. rays by :l si ngle -"Ii t. n) SchemaThe positions of the dark iie-diagram ofslii. b)
aJ

b sin

~=nA,

(5,9)

lens.

\lv'here ~ is the angle between the normal and the given direction, n - an integer, and b - the width of the sli t. A series of furrow" p:lrallcl equi-distant slits of equal width is called a di/Jraction waling. The width of a slit plus the distance between h\o adjacent slits i.t; called the

grating interv!!l. Fig. 73 gives a schematic dcpiction d ~ difTi"ilclion grat. ing. The positions of the fringes 01" 11laX;mU1Tl iiPcn',ity on the screen are determined from the condition (for normal

1I*

164

Cll. V. OPTICS

incidence of light on the graling):

d sin

a~cn'k,

(5,10)

where d is the gralinl( interval. Due to the c1iiIraciion of light waves there is a limit to the alJilitv uf optical instruments to shol'! increasinl;11' greater detail on the "urface of an o';ject at higher ma:inificalions.

aJ

T 1 I

iii£;

the cxlrl'l11e rays from a painton lhe oIJjeet which cnier the oi'je"live and rc,lch lhc ()b~erl'er's eve). DispcIsion of lirzhL The velocily of light in a given medium depend.i 011 the wavelenglh. Tids phenomenon is called

disperSion of light velocity.

!

I

i i

j ;

b}

FUNDAMENTAL CONCEPTS AKO LAWS

1 I

I

Fig. 74. Palh of rays in

f;l~;ss

prism.

The index of refraction al o o varies with

the

wavelcncth

(dispersion of the index of refraction). Due to (hper,ion while lif~hl (\\'hieh consist, of radialion of differenl wavelenl(lhs) is lJro!;cn IIp by a giS'" prism into iis components. Rays of shorter wavelength are IJent towards the base of the prism more siron,~ly than waves of grealer wavelength (F;g. 74). Polarisation of light. In lhe lighl waves emilled IJ'. difTerent 'ources the vectors E (and, hence. If) are o'rien',ed randomly. Such Ught is called natl/ral Ught.

j

Co

---J

!

·-----~:..-----------&'11.'el1

j

Fig. 73. Di!fr"clion of parallel ing. II) Schelllcdic diagTam oi Sibil' direction of the diffraclcd ti cal center of lCll~~. b ~ screen

The srnalle,[ di-iance IJellleen tllO points at which their image" do nol overlap is called the least separation for resolution of an optical inslrument (0). For a microicope the least separation for re:,o!ution is:

I)~ O~~l}" SLlli

('i,ll)

wllere u b the "pertur, ang Ie (hall ille angle suutcndcd by

Fir;. 7G.

Rotation

of

plane of poLtrisation of polarised ray in quartz plate.

It is possib1" (for example, by passing natural light hrough a plate of tOlIflnalinc) to obtain waves in which

166

CH. V. OPTICS

the If vectors will have a sin:J,Jc diredion al a1l points in space. Such wave; are called lillearly polarised (or plane polariscd). In linearly poIMi,''<:d lir,ht each of [he vectors E and If lies in a given plane. The plane of the vector of magnetic field intensity H is called ,he plane of polarisation. Some substances (for example, quartz, aqueous colutions of sugar) have the ab:lIty to .turn the plane of polarisation of linearly polansed hghl pa'3s!nC( through them. This phenomenon is called rotation of the plane of polarisation (Fig. 75). Light can be pari ially polarised by reflection from a dielectric. At a certain angle of incidence the reiiected lioht is completely polarised .. This angle is called the polarising angle. It can lle de;erlllilled from a relation called Brewster's law: tan ip,c~n, (5,12) where n is the index of refraction. Pressure of light. When elec!romar;netic waves strike the surface of a bodv theY exert mechanical pressure upon it (ca lIed the rodit:t iOIl pressure). The magnitude of the radiation pressure is given by

lV'

pc~c (I

+ pl,

T

FUNDAMENTAL CONCEPTS ANI:> LAWS

changes by an amount

£

167

there is an equivalent change in the

mass of the system equal to';;2 (c is the velocity of light). Hence, for every photon emi !ted by a body i is hv reases by an amount t'J.m= c2 •

mass

dec-

Those properties of light which are due to the discrete nature of radiation are called quuntum (or corpuscular) properties. Light, like all other forms of electromagnetic radiation, possesses both wave and corpuscular properties. The photoelectric etJect is one of the l1lanifestatio'ls of lhe corpuscular nature of light. The ell1i~;sion of electrllns from the surface of an illuminated body is called the external photoelectric ef}ect. Laws of the exterrwl photoelectric effect. 1. The number of electrons released per second (or the saturation current) is directly proportional 10 the light lIux. 2. The velocily of the emitted electrons is independent of the light intensity, and is determined by the frequency of the incident light. The velocity n;ay be determined from the equation

(5,13) (5,14)

where lV' is the quantity of radiation energy incident normally on 1 cm" of surface per sec, c -- the velocity of light, P ~ the relJer·tion coefficient. The pressure exerted by the sun ',; rays on a bright day is equal apprOXimately to 0.4 dyne,m' (4 X 10- 5 dyne;cm 2). 5. Quanlum Properties of Light The energy of any form of electromagnetic radiation including light, always exists in the form of discrete portions: These. portIons of energy, "'hlch possess the properties of matenal corpu<'lcs, ilre called radiution quanta or photons. The energy of a photon depends on the frequency of the radiation v. The energy of a photon E=hv, where h=6.623 X 10- 27 erg sec. The constant h is called Planck's colis/ant. . According t? the, fundamental priIriple'; of modern phySIC:; (theory c, lelallVJt)), wh"nelt:r (he energy of a system

where hv is the energy of a photon, If - the work function (see p. 114), m - the mass of the electron, and v - its velocity. Equation (5,14) is called rills/ein's . 3. For every substance there a frequency below which the photoelectric eiTed is not observed. This critical frequency is called the photoelectric threshold (vcr)' It is determined from the relation

hvcr=rf·

(5,15)

When semiconductors and dielectrics are illuminated, some of their atoms may lose electrons, which, however, (in contradistinction to the external photoelectric effect) do not escape through the surface or the body, but remain inside the body. This p[;eno:llenO!1 is called the internaL photoelectric etJect. 1\s a re,lllt of ti1e internal photoelectric effect the resistance of sC!ilicol1 :uclur·; an, dielectric; decrea;es upon illumination.

168

FUND.~ME:t\TAL CONCEPTS

CH. V. OPTICS

When the interface between a metal and a semiconductor is illuminated, an electromotive force arises. This phenomenon is called the harrier-layer e{ject. Photoelectric cells, photoconductive cells, barrier-laver cells and solar batteries are based on the photoelectric phenomena. The photoelectric cell is ba",ed on the external photoelectric effect. It consists of a sealed glass bulb containing a light-sensitive cathode and an anode. The cathode is a thin film deposited on the inner surface of the bulb; the anode is a ring (or disc:) placed in (he centre of the bulb. The two electrodes are connected throUGh an external batterv. When the cathode is illuminated a galvanometer' in the circuit registers a photoelectric current: i'l =v rD -t- io' where t1J is the flux, of radiant energy, y - the integral senszllVzly of the photoe lect rIC ce II, i o - the darll current, i.e., the current in the phoioelectric cell in complete darkness. Photoelectric cells which arc Lased on the in1ernal photoelectric eHect are called photocond'ic/ive cells. The sensitivity of photoconductive cells is characterised b v the specifiC sensitivity (/(). This quantity is equal (0 (he' ralio of the integral sensi'.ivity to the applied potential difTerenee U, i.e., 7 /

i ,j>

\ ."'" {jeD

Photoconductive cells are ;]iso characterised by the magnitude of the ratio R d where Rd is the resistance in the

R---;:'

dark and R,j, is the resistance upon illumination. 6. Thermal Radiation Heated bodies emit invisible waves (so-called ultraviolet and infrared rays) in addition to visible light. The radiation of heated bodies is called thermal (or heal) radiation. A body which completely absorbs all the radiation incident on it is. called a hlach /:ody (or perfect absorber). A hollow box with a small hole in it is a black body. The rate at which a body radiales energy of a' given wavelength from unil surface of the body is called the

AND LAWS

169

emissive po,cer or emissivity :-It the given temperature (F)). The fraction of the incident radiation of a given wavelength 'A which i" absorbed bv a body is called the ah.'orptive po,~'er or at)sorptivity (A)J. 'The emissivity at a given temperature is proportional to the absorptivity at the same temperature (Kirchhoff's law):

(5,16) where f\ at a given temperature is a constant for all bodies.

I

In the U.S.S.R. the quantity

F ie . e)] is called the speetfA

1

•

ral emissivity, For a black bocl\' A;c=l and, hence £;,=10;. for all \\3\'e· lengt hs. The rate of radintion of energy of all wavelengths from a biack body (E) is proportional to the fourth po\\cr of the absolute lellipera(ure (Slefan,BoUZllJann's lim): 1'=-01",

where ihe coefl1cicnt waH/I'm' degree'.

of

(5,17)

proportionality a=5.G7x 10-"

7. Types of Spectra The dependence of the intensity of radi:-ltion of :-I on the wavelength (or frequency) is called the spectmm radiation. This dep2ndenc-e is usual'y depicted in graph forlll, For example, Fig. 76 gives the spectrulll of thermal radiation of carbon for different temperatures. This spectrum closely resembles that of a black body. It is evident from the figure that at any given tempera. ture there is a certain wavelength (f'max) for which the energy of radiation IS a maxirnwn. For a b lack body the wavelength corresponding to the maximum energy of radiation is inver-;el.y proponional to the absolute temperature T (Wien's law of displacement):

AmJ,T=C,

(5,18)

where C is a constant, equal 10 O.28~)8 em degree-I The coioured band obtained when light i, broken up b v 3 prism (or other device) i,; sometimes cidled a spectrum '( i" the nanow sense 0/ the word).

1

170

CH. V.

OPTIC~

Heated solids emU a continuous spectrum in which all the spectral colours are present, one colour merging gradually 'nto the next

1 I

TABLES AND GRAPHS

171

The spectra of heated gases and solids are called emission spectra. If the radiation emitted by a heated solid is pacsed through a vapour, then in the continuous spectrum of the body dark Jines appear, at wavelengths corresponding to the lines of the emission spectrum of the given vapour. Such a spectrum is called an absorption spectrum. Gases absorb radiation of the same wavelength as they themselves emit (law of Kirchhoff and Bunsen). The so-called Fraunhofer lines in the solar spectrum (see Fig. 78) are absorption lines due to the absorption of definite wavelengths of the continuous solar ,peetrum by vapours present in ,he atmosphere.

TABLES AND GRAPHS

Table 98 Relative Brightness Sensitivity (K)J for Daytime Vision (see Fig. 79)

.1/'//ruwiJlet

/"LweI?

Wavelength,

LI?/I'orett 1'6'9/{J/7

1\ :-

A "

Fig. 7G. Energy distribution in spectrum of inc':Hldcscent carbon at di ffcrent temperatures.

.In line
4,000 4,200 4,400 4,600 4,800 5,000

0,00041 0.0040' 0.023 0.060 0.I:J9 0.323

II

5,200 5,400 5,600 5,800 6,000 6,200

.noll

oO . .1,)·1 :

g:~i31

0.631 I 0.381

I

6,400 6.600 6,800 7,000 7,200 7.400 7,600

0.175 0.061 0.017 0.0041 0.00105 0,00025 0.00006

Note. The values of the relative brightness sensitivity are different for different people. They do not vary. however, too widely for people with normal vision. The tahle gives average values of 1\)",

l

I

8/lOIIUIIOl1iW6,5/kJ MW

, ,

I

~

,~

,= SlkIillllJ lilJllllf/

,

IiIIIlSSIVllJ

,

Illrrillm

, ,

-,

/If$t;pu

,

H/!rupt't/

, ,

&tvm

•

"'~

:'*l'CIIl'j'

or emiuion or some ~.,.,>: j"O IlC"''' on top ore the vovol,nl/lh. in anI/strom unHo( ) .

, , • ,If F;I/. 78. Sol_, 'p«trum with I'r.unltorer li_.

172

CH. V. OPTICS

...

I,: :~

k~ U!1l'llno,0/: .~ I ~~ I

~:

~ I ~ I ~I ~I l~';;I~J~I~l ~I1<:$1

/.0

0.8 0.5

I

I

I

I

I,:

II II

1 I

0.4

1 I I 1 ·I-V

0.2

o

,Jooo

I

I

I

:~

:I"

1

:

Illuminance in Some Typical Cases

I

I ~ i"-

~ooo

Table Wi

l{i 1"'2 1

. I

SOOD

4000

,I'M

I

~

I

I

)0

;"11

1000

Fig". 79. Curve of relative brig-llillC'SS :;cllsitivity

for dayli me vision.

Table 99 Luminance of Some Illuminated Surfaces Illuminuted surfuce

Table 102 Reflection Coefficient (,p) of Glass and Water for Different Angles or Incidence (in 0/0)

r (ni tru~;t'lJ)

helium . .

-

, ~ngle o[ incl·

~

Luminance, c£lndc las,/m 2

Substance Caoillary of superhigh pressure mercury arc Carbon arc crater . . . . Metal fj lament of incandescent lamp Kerosene lamp flame . . . Steari 11C cand Ie flame Moonless night sky Spa!k disch;lrge in xenon

0.2 II,Oiill3

5-2 10-15 :lx 10 ' 2. 5X 10'

Table 100

. . . . . . . . . . . . . . . . . . .

211-~1I

C<Jllde]as/m 2

Luminance of Various Light Sources

Surl

1011,0011 1II ,0 110 1,11110 1110 1110-2110 3 0- ~)O

Sun's rays at noon (middle laU tudes) During film shooLing- in studio . . Open area all a cloudy day . . . . Light room (ncar \vi ndo\\') Work lable lor delicale operations I II umi nati on necessary for re;;di ng Cinema screen III umi nati on from fLl 11 moon . Illumination from moonless night sky

Lumin
Cinema screen " . Sheet of \vhite paper (under illuminance 3050 lux) Sno\\' in di feet sunli gh t . • . . . . . . . . . Moon's surface

Source

173

TABLES AND GRAPHS

.

1';1 :lol

15X 10' 12X 10'·15x 10 8 15x 10' 1.5X 10"-2X 10' 1.5X 10' 5x 10 3

Glass Water

0

I Hoc I ,I, ,1,,1;1,1"" 0""' +" ,\0 SO I GO

70

80

S(J

90

I

.

4.7 2

L

2"14.vl".Jj,j"T'O'O

3V

91

100

10

1.IXI0I1 1.5Xl0 11 2.lxl()11

tioll 1.5, ?~: 2.5 at 11orm£1} incidence, For gl:ISS \viP] :1 film 01 sIlica

1 .;::, ><

of iJidex of refraction 1.0. I)

10 12

Note. For glass covered

wi til a film of si Ii ca

of index of refrac·

0.0 at llurnu! illcidcllce.

174

C~l.

TABLES AND GRAPHS

V. OPTlCS

Table 106

Table 103 ~eflectjon of Light Passing from Glass into Air Angle of incidence

Reflection of Light by Metals The figures in the table indicate the fraction of perpendicularly incident light reflected from the surface (in %)

0

100 /10

Angie of refraction

/20+0°135°139+9030' , 40°1600

00<

II

4.7

I

II

15.0 G.8

III II 12

36

47

.c

""§ >-

10°115010'1320/51°163"1790/820/90°1-

Fracti on of reflected energy itl % ·1.7

oj

~ ~

EC :::.::

UltraViolet

Table 104

<.::

1,880 2, 00 0 2,510 3. ~) 1 ~) III

Visible Colour

I

Colour

1< II 3,800-4,500 4,500 --1,800 4,800-5,100 5,100-5,500

cllowish-grcen Yellow . . _ . . Orange. . Red . __ . __ Y,

I

B

OJ

~

2

U

25 31 53

23 31 2b

(j\

~ ~l

.c:"

, C

'";r: j'§ I u

en

0,_

8

u

-

c:

N

Vl

7,000

8, 000 10,000 50, (JOO 100,000

74 9-1 97

17

G,1

22

73

38

3\1

75

\7 ll;

\8

'i ~\

'\\\

JI

\Ill

55 58 61

34 32

I 55 58 60

90 93 94

89 90 98

G2

95

65 02

9G

I I

A

Infrared

-

35 ,j.!

:n

11 72 83

a,OOO

ol1n~ari cs,

5,500-5,750 5,750-5,850 5,850-6,200 6,200-7,600

.)

I

5,000

22

25

",1

7l)

Wavelengths of Visible Region of Spectrum Bounqaries.

~

E:"

0

100 100

nc,n

Violet " Dark blue Light blue Green

175

97

(;\ fi,)

55

69

56

70 72 94

57

1

RI 93

69 62/ \17

-

I _-._------'--------'-----------'----Table 107 Critical Angles of Reflection

Table 105 Wavelengths of U1~~'~violet Region of Spectrum Name of range

Long wavelength ul travi old Middle wave/engtil u](rilviolet _ . Shod wavelengt Ir ultrav; old Va . ~. ullm ultraVic.:!cL . . . . .

Boundaries,

A

I

Substance

Suhs tance

'cr

I

Effect of R a : : : -

3,150-3,800

Suntan

2,800-3,150 2,000-2,800 < 2,000

Erythemogenic Bactericidal Ozonising'

Water _ . Glycerine. _ . Glass (light crown)

49 43 40

I Carbon

IiI

disu][i de . Glass (heavy fii 1: l) Diamond . . . . .

38 34 :24

Note. The values of i cr (in degrees) given in the Llh]c
1

176

CH. V. OPTICS

TABLES AND GRAPHS

Table 108 Wavelengths of Principal fraunhofer Lines I

Line

Element

Iwave1cn g th,

TaMe 109

Index of Refraction for Wavelengths Corresponding to SomQ of the fraunhofer Lines

;\ Fraunholer line

A

Oxygen

7,185

B

6,870

I-Iyc:lroger;

D,

Wavelength,

6,562.8

IOxygen ISodIum

5,8D5.9

Helium

5,875.6

'" <J

A

D

F

H

j7,590!6,870!5,8DO/4,860/3,970

Carbon dlsulIide Ethyl alcohol. Glass (lIght cro~n') : Water.

~"

6,278.1

.0

D,

:1

en

1. 610 1,35D 1.510 I .

I, 61 7

1.3GO 1. 512 1.331

3~9

1.629 I . ~1(j3 1,515 1.333

1.654/ 1.702 1.3G7 1.374 1,531 1.521 1.337 1.344

I

5,8DO.0

D, E

Iron

5,269.6

b,

Ma.gnesi urn

5,183.6

b,

Fable 110

5, I 72.7

Iron

b,

~

.

Iron, -rnagncsi LIm

5, 167.4 '1,957.6

F

Hydrogen

4,861,3

d

Iron

4,668 4,383.6

Hydrogen

4,340.5

0'

Iron

4,325.8

G

Iron, calci um

'1,307.9

q

Cal,::ium.

4,226.7

h

Hydrogen

11

I Calcium.

I

I

Optical Constants of Metals and Semiconductors

5, I 6D. 0

Iron

b,

f\

B

7,621

Q

C

177

'I, I 01.7 ~)

,DG3. ()

~,S3;3.

(;

Substance

Aluminium Antimony • Bismuth .• Cesi urn . . • Chromium . . ' 0 ' Cobalt (G,OOO A)

Copper Gold Iron . Lead •

Substance

1.28 3.4 1.78 O. 3~1 3.5D 2.21 0.62 0.42 2 36 01

2:

3.66 1.63 1.57

IMercury .. Nickel Plati

nilIn

•

3.70

Potd~sium

1.26 1.83 4. I 6. G5 1.3(; 1,73

Seleniulll . Si Ii CO !I . , S;Ivor.,. Tin . . '0' Tung-sten (5,780 A) Zinc . . • . . . . .

12

I. 62 1.7D 2.07 o OG8 2:85 4.24 0.18 1.12 2.7G 2.12

2.71 I. 86 2. 12 21 1 221 0.114 20.1i ·1.03 O.D8 2.GO

0:

Notes. I. The values of the opti cal constants gi ven I n the table refer to the wavelength ),=5,890 A. unless otherwise indicated. 2. The constants nand k are sOmetimes calIed the index of relrac. tion and the Index of absorption, respectively.

12

3m{.46

178

ell. V. OPTIcS

Table 1n

Index of Refraction cf G"scs

l

Gas or vapouJ

ref r::cti

i il

1>1 (ij]

I

I

:-1'----

I. OOOGOI;

J\ceiylcnc Ai r AmnJonia BCIlZL'lJe

inde'

II Mercurv

(H)(l~~):! II A\c(ll:l1lc' ~\Ji tro,;.',\'ll 1.()(J]SI:lIIJOx:>"F~\'IJ . . . I. Ol)CH50 I, .sCICli! "

Carbon dioxi de Carbon 1etraclJloridc Chlorofurm . . . . Helium. . . . • . Hydrogcn . . . . . Hydrogen disulUde

I.OOJ 'IS.ulfur de 1. qu 1 '. II' T clluri 11!11 . 1. UOOIJJJ "V"ter VdI'CJllr I. 000 i J(j Zinc . . • . I.IJOO GIl II

I

are for a v..'avC'1cng-th corresponding 10 the ycllo\'\! lilll' of sodium (D). and arc corrected for a density at 0° C and 7GO mrn Hg pressure by (fOf

p

rndex of Refraetio:1 of Some Solids and Liquids (at 15° C fer the D-Iine of Sodium Relative to Air)

r:~r~~:~ Ii Index of

III

Diamond Ice 1\11 ca Sugar

.:I

Turaz

SUl)st
I

I n
rcl"r:lctiof1

'''' -III---ro",-

Solids

-'cT

"c.

<::l

h

~

I

i

x

l

I C)

X -CO

\

I

--"---------

_ _S_'l_II_)S_i_a_n_('_e_,_ _,_ _

~

('-or-.. ~:;<

the given l:ras).

Table 112

I

10

~ ....."::)

IJ

Note. The values of the indices of refraction "given in the tahle means of the formula n - 1 =const

"',...,,...,"

Index of refracti on

I. U00933 I.OIi(H41 I .II002D7 I.OOOn2 1.001565 1 . UU 0737 1.002495 1.000257 1. U02U50

I .

1. OUO:j77 Ii

'"

179

TABLES AKD GRAPHS

i .:3 I , I .51;-1 . (,0 I' I .51; !I :.OJ ~

1 ,17 1: 33 1. ,13 1.47

c;:::'.':::

IDM':"":'I'-'~

c::

........ ':'1---"'.:;1'-

Y:;..-<

-I' ~;' ~ L'":: ,') ,:":

I

•

I co

1.0

X
I

I

I

L,": '.;:

I I I :;~

~--\--\~-~ ~~~

\

I

I I

;

C~'=2X)

"'"1'''-;-['_:-:'_ --< _ _ ~ -:'-)

I I

"

C0

I n I':: I':") I.() U')

1_------

_ "1"'--!"'7'1

008

::s"-;<

CC".C

,-=' __

O~'lC'

I,~

CD

1I

(")7:'1--<(>1

I

Liquids Aniline, Benzene Canad:] CarLon

I

I

1. ;:)3

.: I

Etll)'i ,Ilco]'ol

1.110 1 . 3(;:2

],,'1

_ _ _ _ II

CI

I. 51 G

..c:

.fiOI I. S3:l

t.o

1.40 i .,11

,-:.; ~J

J

I. ';:32

'=''1::;)"r ::'1-

Oils

1.590 1. 5114:I, Cedar n LIt .

. I . ,

ChlorofoflTl

1,333

11

G! "

;?;

cj

'c 0

"

(",;

-

~

"

0

:.-~

,-

-

"r.·.

;.J

J 2'

=-- -

-~-

--

-

"S:

18~

iI

CH. V. OPTICS

Table 114 Diffuse Reflection of Some Materials in White Light (in %) Materi al

Cardboard. whi te • yellow Cheeseclot h. .. Fatty clay (yellow) . Materials coated wi th whi te pai nt . . Materials coated with yellow paint . Moist earth . Oil-paper (I layer) . (2 layers) •

60- 70 30 1G

Paper, blotting chocolate colour light bllle _ .. ordinary whi te . yellow . Traci ng paper . • . . Velvet. black . . • . Wood (pine) . • . . .

40 8

22 35

II

Emission Spectra of Some Metals (in Aluminiuml copp.. er c (arc 1 n (ar ) vacuum)

~cE

-c E

Wavelength,

6,S63 5,893 5,351 4,861

A

.", ~§ :J(])

O'i::

17.3 21.7 2G.5 32.7

:g E':?~ Z'=:;::

~~E

5,889.970 3,261

----

3,036

3,093

3,274

3,131

5,895.930 3,4 ()-\

3,072

3,944 v

4,023 v

3,650

3,466

3,345

3,962 v

4,063 v

4,046 8 v

3,611

4,680b

4,663b

5 , 105. 5 gl4 ,078 . I v

3,982 v

4,722 b

5,057 g

5,153.3 g 4,358.3 v

4,413 b

4,811 b

5,696 y

5,218.2 g 4,916. ,I bg

4, G78 b

4,912 b

5,723 y

5,700

4,959.7 g

4,7~9.~)

I

5,782. I y 5,460.7 g

5,085.8

(

5,782.~

5,333 g

4

25 GO- 70 25 22 0.4 40

~29. 51

-37 -45 -54.51

~~

-126 -162 -207.5 -253.5

Q)

co .... ~ ~.::b.D

V:J';:..

I

52.9

l

~¥: ~

100.3

E~ ~ ~c~

r-o._bn

6.75 8.86 9.65 9.37

"ray in the solid. p - the density. For Ii 'lui ds and soluti ons ~"~t= Ipe ' where e is the angle of rotation of the plane of polarisation, 1- the path length of the ray ill the liquid or solutioll. c- the concentratIon by weig-ht, equal to the Ilulllbcr of grams of solute per 100 g of solution. For pure liquids e= I_ 2. The negalive sign indicates that the rotatioll is clockwise if one looks at the liqUid from tIle si de of the source.

5,769.6 ii,

5,790~ J

6,152 0

Notes. The rotation of the plane of polarisation is characterised by the specific rotation ["]t. For solids ["]1=-"- . where" is the angle to of rotation of the plane of polarisation. t-t'he path length of the

Zinc (;:1\'12 in vacuum) -'--_ _~

3,126


~~E-c

I Cadmium (arC)

3,248

I

f-o __ u

I

Sodium Mercu ry (i n flame) lamp) I

(mercury

3,083

Table 115 Speciflz Rotation of the Plane of Polarisation for Different Wavelengths at 20° C

- - - - - , - - ,",-\

I

ft.)

I

70-80 13

"

50

~

Reflection

Paper, bro\\'tl . . . . .

2,1

Table 116 I

I

Materi al

181

TABLES AND GRAPHS

4,925 gb 6, I 03 0 6,3620

5,379 g 6,438.Sr

6,232.00

J

Notes. 1. The wavelengths are measured in air at 760 mm Hg pressure.

15°C and

2. The colours ot the visible li nes are denoted by the first letter the corresponding colour. . of 3. The brightest lines are underli ned

13

3aK.46

1

CH. V. OPTICS

182

Table 117 Luminous Efflciency, Efficiency and Luminance of Some Lig'ht Sources

Luminance. ralldelas/m 2

'rype of Lamp

TABLES AND GRAPHS

I

Table 119

•

Typical Characteristics of Photoelectric Cells

f

Type of cell

UB-I 50-watt,

carhon fila-

ment, vacuum

bO-watt. tungstcn Ii· lament, vacuum 50-watt gas-Ii lIed. tung<.;ten Ii lament 50 lJ·watt, gas-Ii Ilcd. tungsten fi lament 2,00 O-watt. gas-fi lied, tungsten fi lament Voltaic arc Lu:ni nescent lamp

5XIO,'i

0.4

2.5 10

1.6

2,460

15X 1OS-20X f 0 5

10

1.6

2,685

5x I 0'

17.5

2.8

2,900

10'

21.2 25

3.5

3,020 4,000

I 3 X I 0"- 1" X 10' 15X 10 ' (crater)

40

G.4

4

183

Cathode

Filling

Integral sensitivity, p. amp/lumen

I I

Dark current, I'- amp

Operati ng voltag'e, v

Oxygen·cesium

Vacuum

20

O. I

240

ditto

Inert gases

75

O. I

240

80

0.01

240

80

O. I

240

0.1

240

UB-3 UB-4

Uf-I

1.5XIO'

Note. The luminous effidenr!.' is the ratio of ihe total radiant flux to the power ,oj" the currcnt in the light :"Otlfce. The effiriency'of a light SOurce is t1:e ratio of the luminous flux to the current in ihe source.

CUB-3

Antimony- Vacuum -cesium

CUB·51

Table 118 Electron Worl, function and Photoelectric Threshold of Varipus Substances Work function. ev

Substance

G.13-G.09

Water Cuprous oxide • Mica . . . .. Sodium chloride Silver bromide . . . Thor;[;m on tUIlg".,ten Sodium on tunt-rs1cn Cesi urn on tungsten • Cesium on platinum. Barium on tungsten . . • . . . .

5.15 4.8 4.2 3.7-5.14 2.62 2. 10 1. 36 1. 31

I.l

Barium ox; de on ox; di sed tungsten . . . .

.

.

1.0-1.1

Photoelectric threshold. A 2,025-2,040 2,500 2,548 2,950 3,350·2,400 4, '130 5,900 9,090 8,950 11,300

CUB-4

ditto

Uf·3

Oxygenwcesi urn

.

I Uf·4

Inert

100

gases

12,400-11,300 I

13B*

..... Table 120 Typical Characteristics of Photoconductive Cells

Light-sensi ti ve material

<J)

C.

»

I-<

<1>C·A4 <1>C·AI <1>C-52

I

I

<1>C-K2 <1>C-KI

I

'Vi ro·

"'"

<J)

Polycrystalli ne cadmium sulfide . • . • . . . . .

0;;0

4x7

I

IIXII

I 3. 5X7. 2 I 3.5X7.2

<1>CK·MI

I

Single crystal cadmi um sulfide . . . • . • . . .

I

28

I

>~,

~:::

0.>-

C-Il>

~

::J t:

•

~.-

ill

a~ 8 E~~ 'lIu,-2~1

--'C)°~OQ.) C 1---, - - OJ

E~~

"2'g ~ ~

'"

~~§

t:<J)

•••.

u

-

~Q;'

"'~ V)ro

······1

Lead sulfide Bismuth sulfide

~E

:;::E

E CD >

~;j

•

,L-

eU:::.:.. u

>.

'"

'Vi

en

2~~cUbD

~I~

<0>

{/) (j)::i..t::

:€ ;::·v ~o~

10'·10'

500

15

1.2

0.015

I 05·l 0 7

1,000

50

4

0.0\

2,50 0 3,000

300 400

35 140

0.0012 0.014

9 :<

10' 10'

I I

I

0

'"0

::!

fh

I

10 12

Notes. I. In view of the non·linear relation between i and the flux the table gives the value of for which the specific sensitiVity has been determined. The table gives the mean values (for a given current) of the speci fic sensitivity at I lux. 2. The integral sensivi ty of the type <1>CK·MI photoconductive cell is 2 ampflumen at 10 lux and 60 v. 3. The current in the photoconductive cell depends on the temperature: it =:!:.io (I +ot), where i o is the current at O°C, it - the current at tOC, and ~_ the mean temperature coefficient of the current.

.~

-ot""

Table 121 Typical Characteristics of Barrier-layer Photoelectric Cells Integral sensilivi ty, p. amp/lumen

Sensi· live area, cm 2

Llght·sensi tive material

TYre

typical samples

I

best samples

Iniernal resist ,nce, ohms

E Wei·

ency, %

...,

:.-

I

K·5 K·IO K·20 <1>3CC·Y2 c!)3CC·Y3 '1':')CC-Y5 (j)3CC·YIO

· .......... · .......... · .......... sulfi de . . . • . . • • . .........

Seleni um " "

Silver "

"

"

". : : : : : : : : I sui [ide . . . . . . . i

Thallium Crystalli ne si licon (wi tb admi xlure 01 boron)

.....

250 250 250 4,000 4,000 4,0 00 4, 000 o,OOO-G,OOO 15,000

500 500 500 1,000-8,000 7,000-R,000, 7,000-8,000 7, 000·8, ADO 10,000

I

,",000

I

5 10 20 2 3 5 10 2

I 0'-5X I O' I 0'-5X I 0' I 0'·5X 10' I. 5X I 01-3X 10' I X I 0'·2 X I A' 7XI02-1.4XI01 4XI0'-8xI0'

1·8

1·10

-I -I -I -I -I -I I 11-13

tll t" tTl

[Jl

:.-

z

t:I

Cl ;>:l

:."0

u;

Notes. 1. The i nteg-ral sensitivity is gi ven lor the photocurrent in the short·ci rcuited cell. 2. The integral sensitiVity tor the silicon cell refers to an area of G.5 ern'. 3. A system of silicon photoelectric cells is called a solar b:lItery. It is believed that the efficiencY of a 'solar battery can be brought up to 22%. 00

<1\

':',..............~---

_......

T !

FUNDAMENTAL CONCEPTS AND LAWS

187

The motion of the electrons in the atom may be approximately described as motion in circular or elliptical orbits around the nuc\pus (Fig. 80). The,e orbi ts are called stat ionary orbits. When an electron revolves about tlj.C nucleus in

C HAP T E R VI

;'

,.-

STRUCTURE OF THE ATOM AND ELEMENTARY PARTICLES

;'

'"

~

~

I

I

I

.I

,,

,

FUNDAMENTAL CONCEPTS AND LAWS

1. Units of Charge, Mass and Energy in Atomic physics

The unit of mass is equal to 1/16 of the mass of the oxygen isotope (see p. 188) with an atomic weight of 16: I atomic unit of mass=1.66xlO-2< g.

\ \ \

\

\

\ \

\

!.

,, ,

.... ....

f/=! ,"-, { ,_ ....:

... ...

,

... ....

"... ....

_-, ... /

... ....

....

,,

,

"

\

\

\

\

\

I

\

\

\

\

,

•

\rd

I

:f/=J

If/=4.' I

I

I

I

I

I

I

I

-

.' ......... ----,,-" '"

/

t

.-I

I

,.I

.- '" .. _-----,--"... ...

.....

,,

,

,..-- .... ..., '"

I \

\

~

The mass of the lightest atom - the hydrogen atom - is equal to 1.008 in this scale. The unit10f energy is the electron-volt (ev); it is equal to the energy acquired by an electron in falling through a potential difference of I volt. 1 ev = 1.6 X 10-19 joule = 1.6 x 10- 12 erg.

r

I

(

.....

/'

Fig. 80. Possible electronic orbits in hydrogen atom (tlie radii of the orbi ts are in the ratio of the squares of the integers 1 :2 2 :3 2 :4 2 etc.).

a stationary orbit it does not radiate. The radii of the sta-

2. The Rutherford-Bohr Model of the Atom

The centre of th~ atom consists of a posi ti vely charged nucleus around WhICh electrons revolve in definite orbits. The mass of the atom is concentrated primarily in the nucleus. The nucleus of the hydroi~en atom is cal1ed a proton. The mass of the proton equa Is 1.67x 10- 24 g; that of the eleetron-9.11xIO- 2'g(ljl,836th part of the proton mass). The charge of the electron is equal to the elementary charge. The charge of the nucleus is equal to the number of the element in the Mendeleyev periodic system. The number of electrons in a neutral atom is equal to the charge of the nucleus,

'" I \

~,

----- -, ..... ....

I

I I I

I \

~

;'

I

I

o

~

I

I

The unit of charge is the elementary charge: e = 1.60 X 10- 19 coul.

,,-

I

1

-><---- - ---

~'

tionary orbits are determined from the condition h

mvrl/= 2:n: n,

o

~)

(6,1)

where m is the mass of the electron, v - its velocity, r l/ ~ the radius of the orbi t, h - Planck's constant, n = I, 2, 3, .... Every stationary electron orbit (in other words, every stationary <;tate of the atom) corresponds to a definite value 01 the energy (energy level), The energlf {:!ue!s (V:',,) and the radii of the circular orbits vl the hydrogc:n atom can be computed by the formulas;

188 CH. VI. STRUCT. OF THE ATOM AND ELEMENT. PART.

Wn = r ll

=

2Jf}me'

fi2Ji2"" •

(6,2)

n 2 h2 L[Jt2

me 2 •

(6,3)

An atom radiates or absorbs energy in the form of electromagnetic waves when an electron jumps from one stationary orbit to another. The magnitude of the emitted or absorbed quantum (portion) of energy hv is given by the condition hv = W 2 - Wt> (6,4) where W, and W 2 are the energy levels of the electron in the atom before and after the change of orbits. According to contemporary views, the stationary orbits do not actually represent the trajectories of electrons in the atom. Modern physics has a somewhat different approach to the prob lem of the struelure of the atom. However. the concept of atomic energy levels remains valid.

r

FUNDAMENTAL CONCEPTS AND LAWS

Electrons in complex atoms are grouped in shell,. A includes a certain number of eleelronic orbits. At most electrons can move in the same orbit. The shell of least radius can contain at most two trons (one orbit). This shell is called the K-shell. The

189

shell two elccnext

3. The Atomic Nucleus and the Electron Shells The nucleus of an atom of any element is made up of protons and neutrons. The neutron is an electrical Iv neutral particle whose mass is apprOXimately equal to the mass of the proton. Nuclei of the same element may contain different numbers of neutrons, and hence may have different masses. Elements which differ only in the number of neutrons in the nucleus are called isotopes. The mass number (M) of an isotope is the whole number which is nearest to the atomic mass of the isotope. The number of neutrons in the nucleus is

N=M -Z, where Z is the nuclear charge. The proton and the neutron are collectivelv called nucleons (nuclear particles); inside the nucleus these parttcles are mutually transformed one into the other. The density of the nuclear matter is extremely high (about 100,000,000 tons/cm'). A nucleus IS denoted by the symbol of the correspondin d chemical element with the atomic number as a subscript and 2' the mass number as a superscript (for example. Alar 2

13 AI ' stands for aluminium with atomic nUlmber 1313 nd a mass number 27). .

.-

Fig.

81.

Diagram of eleclron shells of tbe atom.

shell !L-shell) can contain up to eight electrons. the following shell (M-shell) - up to eighteen electrons. Th~ third shell is subdivided into two subshells iVl] and M." which can contain up to eight and ten electrons, respectively (Fig. 81).

4. Nuclear Transformations When a nucleus s formed by bringing together a certain number of protons and neutrons the rna,;s of the resulting nucleus is less than the sum of the masses of the component protons and neutrons. This dif1'erence is ca lIed the mass deficit of the nucleus. The energy reledlsed when neutrons and [Jrotons combine to form a nucleus is called the binding enerfl:!J of the nucleus (E). In computations one usually deals with the quantity E;M, i.e., the blllding energy per nucleon. fhe average value of the quantity EjM for heavy nuc leI is taken equal to 8x106 ev,

.....

<1

190 CH. VI. STRUCT. OF THE ATOM AND ELEMENT. PART.

. Some heavy !1l1clei (uranium, thorium, radium) spontaneously dlslntegrate with the formation of new nucle: and the emission of a-particles, electrons and high-energy photons (v-rayssee .the . e~ectromagnetic spectrum). This property is called radlOactl vtt y. The law of radioacti \'e decay is t

-y

r

i

(6,5)

N=N o2 where No is the ori~inal number of nuclei present at time t =0, N ~ the number of nucl,:,i left at time t, T - the half lite, equal to the period of time at the end of which half of the atoills of the radioactive material will have disintegrated. .

191

TABLES AND GRAPHS

5. Wave Properties of Matter Every moving particle possesses wave properties. For example, when an electron passes through. a me.tal film we obtain a diffraction pattern similar to the dIffraction patterns of X-rays and V-rays (Fig. 82). The wavelength of a particle is determined by the relation

'A=~.

(6,6)

mv

where m is the mass of the particle, v - its velocity, and h ~ Planck's constant.

, TABLES AND GRAPHS

t

Energy Levels of the Hydrogen Atom The energy levels are calculated by means of iormula 16.2) by substituting ior n the successive integers I, 2. 3, 4. etc. UtiliSing the energy level diagram it is easy to calculate the irequenl'les of the spectral Ii nes of the hydrogen atom by means of formula [oerpv,ev (6,4).

cj Fig. 82. Oi ffrJclioll oi 0.) X-rnys by a polycrystalli ne gold fi 1m, uJ electrons by a polycrystalli ne gold fi 1m.

Nuclear transformations may be ind uced arti ficla Ily by bombarding elements with protons, neutrons, helium nuclei and v-rays. Such transformations are called nuclear reactions. Nuclear reactions mav lead to the formation of new rad ioactive isotopes, which cia !Jelt occllr naturally on the earth. This phenomcnon is called artificial radioactivity. Nuclc,ar transformatiom are utilised to relea-;e nuclear energy by the fission (splitting) of heavy nuclei (for example, 23 U ,) or by the synthesis (fUSIOn) of light nuclei (for example. hydrogen nuclei). The synthesis of Ii~"ht nuclei requires extremely high temperature. (of the n,-der nf Illi I lions of degrees). Such reactions are ca! led I her fllunur.:!t;ar.

When electrons jump to the level n= 1 the atom emi ts a series of Ii nes called the Lyman series; the Ii nes of thi s series lie in the ultraviolet reg-ion of the spectrum. Upon transi tion to the level n=2 the ii nes of the Balmer series are emi tted (four. Ii nes of this series lie in the visible part of the spectrnm. the remainder-in the ultraviolet.) Upon transi lion to the level ,,=3 the lines of the Paschen series are emi tted Ii nirared region). The numbers near the short arrows in each series i ndi cate the o longest wave· length Ii A) in the given series (l A=IO-'cm).

I.

14

IJ .-/1 II

JfJ

iSu/mer !Jenes

9 8

7

6 S

J 2

o .L----l...L.'-Fig. 83. Energy level diagram of hydrogen atom.

L?mufJ ff(fe~:,

-=-n'(

T

CH. VI. STRUCT. OF THE ATOM AND ELEMENT. PARr.

I

3 "

6.940 11

Na

III

22.997 19

IV

39.100 29

4

, I'•

V

Mg 24.32

7

.

18

II

Ag

•

107.880 55

,

18

CS

18 8 1

132.91 79

I

•

18

31

Au

18 8 1

197.2

I:

Fr

i

59

I

l i~ Nd

140.13

1

1

"

91

18

Ii I

Pa 231

, "~~ U 1

: TI 2

44.96 31

3

"•

Table 122

t

t

56

or

TABLE

ELEMENTS

GROUPS

57

I

Ii" I

Hg 200.61

,

2

18

nAc

226.05

61

11

Ii

2

62

•

150,43

1

8

13

Np

: [237)

• 1

As 74.91

1

I

41

:~ Nb

11 18 8 1

92,91 5

51

1:

Sn 1

73

I

2

I

n,

Pb

209.00

:~ Pu

~ [242J

94

2 13 8

1

Se "

li Tc I [99] 1

52

,

1 13

43

28

NI

!

I

44

Ru

il

1

, 2

""•

" Pd

I

: 102.91

106.7

1

Xe

" 18

77

1

"

Os

31 18

• 190.2

Ir

• 193.1

1

78

1

15

,

Ii !

1

PI

'·i·

19U3

,., 8 1

I II 31

" 8 1

86

85

",

8 2

18

131.3 76

8

"

0

46

11

126.91

Re

7

36

8380

,

45

Rh

31

Po

31 '8

AI

Rn

1

210

1

[210]

222

8 18 31

18 8 1

(Pa) lU)

2

63

•

'lANTHA l 64 ; '

:: Eu

ii

: 152,0

1

1 8 11 31

18

• 1

95

Gd

• 156.9

..

243

• , 1

ACTI

1

8

15

Am

:i

11 Cm : (243]

96

1

tilDES

8

1

66

8

,

Te

:: Dy

159.2

2

1 8

67

i: Ho

162.46

1

68

8

:: Er • 164.94 , 16/.2

1

1

69

1 8

:3

1

,

70 71 :i•• Vb 31"• Lu " , 173-04 174.99 • 1

9 31

Tu

• 169.4

8 1

1

1

N 1 DES

15 31

"

1

65

(l7

, 2

11

Bk [245)

Ii Cf ! [246]

98

1 8

99

"iij En •

100 1 101

Fm

I

IMd

I 256 255 1 253 NUMBERS OF STABLEST ISOTOPES

I I

t I

102

No

ATOMIC

I NUMBER

I

t

I

8

1,

54

1 13

,

16

58.69

I

"•2 186.31

", "

1

15

58.94

Kr

1

75

1 II

183.92 6 84

27

Co

53

1

31

I

"• 101.7

Te :: 127.61

t.

55.85

79.916

I

42

26

Fe

Br

'78.96 :

W

,

25

-

Ar

35

1

74

BI

!

207.21

"•1

1

I 2

Mn

1

18

39.944

35.457

: 54.93 34

6

",

5 18

i

1 I)

31 18

180.88 83

82

24

52.01

CI

I

I

8

20.183 "

17

S

1

10

Ne

19.00

1

n066

Cr

F

1

16 6. 8 1

9

0 16

1

6

11

:: Ta

•

18

121.76

10

8

95.95

Sb

I

2

He 4-003

Mo

8

1

93

11

1

,

,

2

18

~; Sm

1

1

•• Ii lTh}

: 227

60

72.60

178.6 I

204.39 1 89

33

I

" TI Ii

+

•

88

92

I

138.92 81

5

~8

:: Hf'

3

I: 50.95 V Ge

72

9

P 30.975

23

118.70

2

15

2

~"

I

VIII

VII

N 14.008

I

50

In :: 114.76

1

!

1

91.22 I

',8

2

137.36 80

Ii I

I

7

SI5

40

Zr

1'8

• :: La •

1 18

14

32

1

Y

C 12.010

1

88.92 . 3 49 18

Cd

6

47.90

I

103

lH)

28.09

I: 69.72

39

1I2.41

,

Ga

2

48

Ba

~ 238-07

V

22

1

Zn

v"".

2

: Sc

• 140.92 • 144.27 1

21

2

nRa

:: Pr

Th 232.12

30

1

I

Ce

90

20

18

!"

(223]

08

I

26.98 :

I

1 18

•

87

X

AI

21

13

2

8

IX

23

"

"8

1

6

I 1

2

I85.4847

VIII

10,82

12

l

1 18

B

23 22

9.013

65.38 II •I: Sr 38 87.63

VI Rb VII

5

63.54 37

~

Be

2

Cu

1

5

4

l Ca I 40.08

K

IV

TABLES AND GRAPHS

VI

'. 1

~

Li

"'

-

I

1.0080

II

2

II

1)

H

MEtfOHEV'EV'S PERloblc ELEMENT

I

, 1-

oI

-

~

PERIODS SERIES

'.~

SYMBOL

I AT 0M I C ......=:.:-~"--'-' 253' WflGHT ElECTRON

SHEl.\,.--S..

tal ns the symbol of an element; above i t ~the atomic number. below most Widespread isotopes). The columns oHligures gIve the number

J94

CH. VI. STRUCT. OF THE ATOM AND ELEMENT. PART.

Table 123 Relative Abundance and Activity of Isotopes of Some Metals

T , ~

TABLES AND GRAPHS

Table 124 Atomic Weight, Relative Abundance and Activity of Sonie ___~ ~_L_i-"g~h~t_lsDtopes. --, _ Element

Number of protons

EJement

Number of

neutrons

Relative abundance.

%

Half life

26

32

i

Co

eu

I

26 27 28 29 30 31

27

29

33 28 :!9 30 .31 32 33 34 29 31 32 33 34 3'"

3G 37

-

Type of activity

H D

-

6.04

91. 57 2. II 0.28

100

-

-

-

09.48 30.52

-

7.8 hr 8.9 min stable 4 years stable

He

0+ I'

~ ~Il :0

"'0

T

Fe

I 1 I 2

~+

C

6

(J

weight

~

7. 7, 7. 7. 7·

~

7, ~

ij

-

~+ ~+ ~+ ~+

-

-

o

8

1.00~t

7 R 7

2.01H 3.0170 3.0t70 4.0039 5.0 t:17 Ii. 0209 to. 11.01 12.0039 13.007 Ii H.OOn loS. ()n 7,~

B

1 G. ()()(I()

1 2 3 4

4

9 10 II 13 13 Al 14 1S 16 /Vote. ~ - - electron. nucleus. n -neutron.

I. 3 -,

9 ~. () 1.1

stahle

76 . 0.04 0.20

25.99-14 26.9~J07 27.990~

tOo

28.9892 ? + - posi tron.

n

a

, 1

years

l~ec

stable

31 "sec 7 sec stable 2.;) min (i.7 "( - gamma-rays.

Some Artificially Produced Elements

ij+ .,+

v

10"~~o sec

~+

I'

8+

r...-

. 8 sec 0.8 sec 21 min stobIe

10'-t D~.

ot

activity

12.5years stable

~lOO

17.0045 18.0048

Atomici number

Name of element

61 85 87 93

Promethium (Pm) Astatine (At) Francium (Ff) Neptunium (Np)

94

Plutoni urn (PU)

95 96 97 98

Americium (Am) Curium (em) Berkelium (Uk) Californium IU)

243. 245. 24ii, 247 244, 241i. 248

99 100

Einsteinium (En) Fermium (Pm)

2[)3 255

-

1

cr. ~ helium

Table 125

l\1ass numbers

.'

7. (4~-

:3

-

145.1 H7,148.1'19,1;;0.IGI 21Hi. 209,~IU.2tl 212. 221, 222, 223 231,232, 234,235,236, 237.238, 2:32,23-1. 2:Jli. 237, 239,240, 241

Note. See note to the follOWing table.

99.98 0.02 2

Ty!'e

Half Ii Ie

~~E;.

c'

0 1

:::

~.g*

Atomic

5 Ii

.

" 47 days 18. I hr 8 days 270 " 72 " s(able 5.3 years 1.75 hr 7.9 min 8.1 sec 3.4 hr 9.92 min stable 12.8 l1r stable 5 min

195

101 102 jVotf? is given

24 ')

30 vears

~.3·hr

2 I min 2.15XIO' Years 5'XIO'years

'l.l ')

2:J~:2:19~~-1(J·.241.242.243,244 10' years

2:l8,240,241.242.243.2H,2~5 GOO years

5 days 2,IOOyears

Mendelevium (Mv) 2,)(; Nohelium (No) 2G3 Tbe mass numher of thE' i .c:olo;~c \Vi tll the grC';:ltest in boldface type.

half life

Inti

CII. VI. STI'
Tahle 126 Elementary and Non-Elementary Particles Particles which, according to present-day notions, are not cornpcsed of lJlore fundamental particles are called elementary.

Energies of Some Particles Particle

197

Table 127 Energy. Mev

Mass Name

Maxi mum energy of i3 - (Th C -> Th C') • " ij- (Th C" -> Pb) Energy of cr-parti cle (Th C' -> Pb) • • a-particle (Th C' -> Th C") • photon of "(-radiation . " cosmic ray mesons (secondary radiation)

Average lifetime, sec

Symbol

Particles produced in accelerators

Elementary

Protons . . Neutrons .

particles

Photon

h'l

j',

v v

Kcutri no Anti neutri no

Electron

P-,

Posi tron

e+,

L-mesons

;+

0 <0.001 <0.001 I J

0 0 0 -I +1

210 210 275 275 300

+1 -I 0

9GG 9GG 965

+1 -I 0

stable in vacuum 2.22XIO-' 2.22XIO-' 2.53XIO-· 2.53XIO-· IXIO-'·;-5XIO->5 1.27XIo-a l.27XIO-' 1.3XIO-'o

1.007GO

1,83G

+1

stahle

1.00899

J,839

0

7XIO'

10- 3 0- 3 1 155

O. I 155 0.151 O.IDI O. 1GD

~+

.

_0

1'UclCOllS:

0 0 0 '5.4 15.

n.

11.+ IJ--

K-mesons

K+ K!(~,

1{2 0

pro Ion

P. II'I

neutron

n,

tl

1

u

+1 -I

Antiproton

p

1,836

-I

Anti neutron Hyperons

n

1,839 2,181.5 2,327 2,327

0 0 +1

Non-elementary particles

1\0 1:+

,,1f2

stable

-I

3.7XIO-IO 3.4XIO-u 3.4XIO-u

Deuteron

d,

+1

stable

t, 1'3 'I

3.016

+1

d, IJc~

4.003

+2

17.G9X X3,GOO stable

1

2.014

1t+~mesons tt- -mesons

p.+-mesons -mesons . . . . " '" . Photon of 7-radiation (i 11 dc','ay of ;-:o-lllc:;ons) • r-radi'ation (in decay of deuterolls) • • r-radiation (in decay of cr-particles)

IJ.-

I

GO 0-700 500-G50 I GO-360 300-400 90 25 la-GOO up to 30Q 500-GOO

Notes. J. The nuclear reactions in which particles of the given energy are produced are gi ven in parentheses. 2. The i ndi cated energi es of particles produced in accelerators were obtained in the USSR in the G-meter proton synchrotron (as of July 1957). More recently protons of energy 10' Mev were produced In the high-energy proton synchrotron in Dubna. The maximum par.. ticle energy obtained to date is about 3X10' Mev (proton synchrotron in Geneva).

stable in vacuum

Triton Alpha-particle

2.25 I. 79 8.95 G.20 3.20 10-- 3 -10'

Notes. I. Mesons and hyperons are produced in the collisions o[ high-energy particles (for example. protons and cr-particles in the
Table 128 Energy of a Quantllm of Radiation of Different Types Wavelength

I

~

1 mm 300 I" I I"

8,OOOA o 7,000 oA G,200 A o

5. oon 0 A 4, 000 A o

3,000

A

Energy, ev

\Vavclength

Energy, ev

1.22XIO-3 4. I Xl 0- 3 1 22 52 1.75 1.% 2.44 3 OG 4. 10

I,OOO/,.. 100 0 A 100A

J.22XIO J.22XIO' J. 22;<1 0' J.22XIO' 1.22;<10 5 I. 22)<10 7

I:

I A

0

O. I A o 0.01 Ao 0.001 Ao 0.0001 A

1.22XI0 8

.,... 198

CH. VI. STRUCT. OF THE ATOM AND ELEMENT. PAHT. Binding Energy

On the abscissa axis (Fig'. 84) arc plotted the mass numbers, on the ordinate axis - the binding' energy ElM per nucleon in electron volts. Knelear encrg'V can be released either by the fission of heavy

~ !le/illm(7!lIfV),_ _-_~ 8

I ~

I

'TABLES AND GRAPHS

199

Synthesis of Helium from Hydrogen Tbe production of helium nuclei by the synthesis (fusion) of hyd. rogen nuclei is of immellse thc(lrctical
I

8.8111er

7

1

{/;'i11l1i/1Ii(:;:J11Ievj

8 5 Reactions of Nuclear Synthesis J

Reactions of nuclear synthesis can take place ci ther at hig'h temperatures (millions of degrees) or at high field intensities (millions of voltS). The follOWing are some examples of such reactions.

C

!Jeli/edu/ll (1. IJ.9mfvJ ll-_ _-I-,--_ _........ 50

{OO

-

150

_ _+ - _ ~ . . _ . . _ .

2CO

250

11

Fig. 84. Curve of binding energy.

Iwclei or by the synthesis of light nuclei. In both cases new nuclei are produced with a binding energy ElM greater than that of the original nuclei. Examples of Nuclear Reactions Nuclear reactions are accompanied by the rclci1sc or absorption of energy. In the re:lclions g'iven below the nnmbers on the left·hand side of the equations indic;:te the energ'V absorbed, on tbe right·hand side of the equations - the energy released. in Mev.

Notes. 1. The arrows in N]ll:l/ioll G indicate th.1t 1I1C reaction ('on~ tinues spontnnco~lsly. 2. The fis:sioil of one uranium 11llc]ell~_; ]c;lds to the release oi about 200 Mev ?f encr.l':Y· The energy released by I gram of uranium equals 22X I OJ kiiowatt·bours.

~

I [

/Jnits of Radioactivity and Radiation The unit of radioactivity is the curie. I curie corresponds to the Intensitv of radiation of radon in a state of radioactive equilibrium with I gram of radium. The curie is also a measure of the quantity of a radioactive substance. A curie is a quantity of any radioactive substance which decays at the rate of 3.7XiO'o atoms per second. The roentgen is the unit of X· and ,-radiation. A roent[!.en is a: quantity of radiation which produces in I em:' of dry air at O°C and 760 nltn Hg a number of ions carrying a total of one electrostatic unit of charge of each kind (2XI 0" pairs of ions).

a:;:w.. 20:

APPENDICES

APPENDICES

The deviation L'.Ai= I Amean - Ai I is called the absolu!e en'or of a single measurement. The quantity 'A -_ ---~-------~--L'.A I L'./1 2 !\/l" • L.l n is called the mean absolute error of the measurement. Usuall'Y it is considered that Arrean - L'.A < A < Amean L'.A.

+ ... +

-+

I. I;ome Frequently Encountered Numbers n=3.1~1593 Vn=1.77245

4n=12.L16637 2 n =0.63662

e=2.718282

V2= 1.41421

13 =

n 2 = 9.86960

1°=0.017453 radia 1'=0.000291 n I" 0 " = .0000048

+

mean

-

I

---

I

YI+x=I+-x 2 I

I

Vl+x=I-Z-X

is called th·c mean relative error and is

usually expressed in per cent. The result sought by the experimenter is rarely found by measuring only one quantity. It is generally necessary to measme several quantities and to calculate the desired result from a formula. The following table gives expressions for finding the absolute ane! relative errors of calculations carried out by some frequently encountered for-

1.73205

II. Formulas for Approximate Calculations

l+x=l-x

AL'.A

The ratio

0.031 0.085 0.052 0.077 0.045

< x < 0.031 < x < 0.093 < x < 0.052 < x < 0.077 < x < ' .045

mulas. Formula

Absolut~

Relative erro:

error

sinx=x

e"'=I+x

t

A13 A

perfor~edJ

An

All measurements can be only up to a certain d egree of precision. Precision is determined b' tl1 I .. the measurement. In order fo e : I.. ~st slgnIfkant Ilgure of are always possible the .. c " e chance errors which several times and 'th measur.ement should be repeated results taken. e mean arIthmetic value of all the 'd

+ A +... + An 2

fl

iA\+iB1

I B IlA -f-A1B I

m+1BT

AA

13'

n\ A

n1

j A

n_

113

AA

nm

1

\ AA

l-n n

1..1£1

Example. To determine the density of a solid one measures its volume and its mass. Assume that HIe volume has been measured with an accuracy of 1.5 % , and the mass with an accuracy of 1"/0' Then the relative error of the determined value of the density is 2.5)/0' Hence, we may write:

If a quantity A has been measured n t' As, ... , An are the results of th . d' . lmes and A" A 2 , then the mean arithmetic value eislO IVldual measurements,

= At

IAIlB+B1AI

73

III. Elements of the Theor\l of Errors

mean

\A-BI t>A 1113

A~13

The inequalities indicate tho r1 whIch the error of the t ran,e of values of x for formulas does not exceedcgn l?,L1 a IOns by the approXimate . l 10'

A

A+B l ~\ IlA+t>B

IlA+IlB

A+B

1

V (!!!-)

14

(1 _ 0.025) mean

3aK.46

<

}11_

V

<

(!!!-) V

(I mean

+ 0.025).

13

:::

202

,

APPENDICES

IV. Prefixes to the Basic Units of Measure mega (M) 10" milli (m) kilo (k) 10 3 micro (~) deci (d) 10-' nano (n) centi (c) . 10- 2 pico (p) .

I 10- 3 10-' 10-· IO- IZ

The figures in the right-hand column indicate the number of multiples 2nd sub-multiples of the basic unit which are formed by attaching the prefJxes. For example, 1 Mc/s = 10' cis; 1 mm = 10-' m. V. Uoits of Measure of Some Physical Quantities Mass ton = 10 centners = 1,000 kilograms. carat = 2 X 10-' ki logram pood = 16.38050 kilograms.

4._._.5

c;::::e.,

APPENDICES

203

Thermal Conductivity 1 kilocal/m hour degree = 2.778 X 10- 3 caljcm sec degree =

= 1.162X 10- 2 watt/em degree.

Work and energy watt-hour = 3,600 watt-sec. joule = 1 watt-sec = 107 ergs . 0.239 cal (calorie), kg m (kilogram meter) = 981 Joules. j'ilocal (kilocalorie) = 1.16 watt-hours, ~v (electron volt) = 1.6019 X 10- 12 erg=1.6019XlO- 1O joule. Power watt = 10 7 erg/sec. kilowatt = 102 kg mlsec = 1.36 hp (horsepower). Capacitance

Length 1 micron = 10- 0 m. 1 A(Angstrorn unit)=IO-8 cm . 1 X=--= 10- 11 cm. 1 inch =--= 25.40 rnm. 1 foot = 0.30480 m.

1 yard = 0.91440 m. I mile (English) = 1,609 m. I mile (nautical) = 1,852 m. I light year = 9463XI012 km.

Time year=31,.5,56,925.975 sec. day=24 hours = 1,440 min =86,400 sec. hour = 60 min = 3,600 sec. Pressure 1 atmosphere (technical) = 1 kg/cm 2= 735.66 mm Hg. 1 mm Hg = 0.001316 atm = 1,33~ dynes/cm 2= 1333 nt/m!. 1 atmosphere 6 (standard) = 760 mm Hg = 1.033 kg/cm 2 = 1.013 X 10 dynes/cm 2= 1.013 X 10' nt/m 2.

=

Temperatwe Number of degrees centigrade (DC) =--= 5/4 0 R = 5/9 CF _ 32) = =(OK - 273). Here oR denotes the number of degrees on the Reaumur scale, of - the number of degrees Fahrenheit, oK _ the number of degrees Kelvin.

1 em = 1.11 picofarad = 1.11 X 10 - '2 farad. VI. Universal Physical Constants Gravitational constant y . . 6.67x 10- 8 g-I cm 3 sec-2 6.67x 10- 11 kg- I m' sec- 2 Volume of one grammolecular weight of an ideal gas under standard conditions Vu. • • 22.4207 Ii ters Universai gas constant'R 8.31696 joule degree- I mole-I Faraday's number F . . 96.521 couljg-equiv Avogadro's number N . 6.02497 x 10 23 mole - I Boltzmann's constant k 1.38041 X 10-'6 erg degree- 1 Mass of hydrogen atom m H 1.67339 X 10- 24 g 1.67239 X 10- 2• g Mass of proton m" Mass of electron me . . . . 9.1083 X 10- 28 g Charge of electron e . . . . 4.80274 X 10- 10 CGSE 1.60202 X 10- 20 CGSM Velocity of light in vacuum Co 2.99793x 10'" cm sec-I Planck's constant h . . . . 6.62517XIO-27 erg sec Rydberg's constant for hydrogen R H • . • . • . . • 109,677,576 cm- 1 Rydberg's constant for deuterium R o 109,707.419 cm- 1 Rydberg's conshnt for helium R He 109,722.267 cm- 1

11

...... '"...

o

MKSA System of Units The following table gives the names, designations and dimensions of the most frequently used units of the MKSA system. The last two columns give the conversion factors for the CGSE and CGSM systems. For mechanical units the CGSE and CGSM systems coincide fully; the fundamental units of these systems are: the centimeter, gram (mass) and second. The two systems differ for electrical quantities. This is due to the circumstance that the fourth fundamental unit in the CGSE system is the permittivity of vacuum (8 0 = 1), and in the CGSM system - the permeability of vacuum (fto= 1). Conversion factors rela ting MKSA units to Dimensions

Unit

Quantity

J.

Length Mass . Time. Current

· \ meter, m · tilogram, kg · second. sec • ampere, amp

Velocity •. Acceleration Energy and work Force. Power

"""*'

, . . ... Ji. . . .

~:

CGSM

CGSE

Fundamenta: units

m Z

o

(.IJ

10' cm 10' g 1 sec / 10- 1

lO' em 10' g I sec 3 X 10 0

l

kg sec

1amp

2. Mechanical units 10' meter per second, mlsec \ mlsec 102 meter per second per mlsec' second. mj sec' 10' joule or watt per second, kg m'jsec'=joule joule kg m/sec 2 =joulelm 1105 newton, nt kg m'jsec 3 ;;o:joulejsec 10' watt, W

-----

'"0 '"0

n m

m

.....'

:0-

cm'sec' em/sec 2

10 2 em/sec 10' cm'sec'

ergs

10' ergs

dynes

10' dynes 10'

------~----

""!!!II

~-...

.1. Electrical units

Charge . . . . . • •. coulomb, coul Potential, e.m.!. . . . volt, v Electric field intensity . . . . vol/ per meter, vim Capaci tance . . . . farad, fd Resist ance

ohm,- ohm

amp sec=coul kg m'/amp sec'=v kg mJamp sec 3 =vjm amp'/sec'/kg m'= =amp'/sec'/v= =sec!ohm kg m'Jamp' sec3 =

1/3 X 10-'

10 lOs 10'

9 X 10 11 cm 1 '9 X 10 - 11

10-0 10'

13 X 10' 1/300

1

1

=::: v/amp

Resistivity

ohm meter, ohm m

Permittivity

farad per meter, fd!m

Magnetic !lux . . . Magnetic induction

weber, \Vb weber per square meter. wb/m' ampere per meter, amp/m'

li9XIO-ll

10"

9 X 10'

10- 11

kg m"amp sec' kg'amp sec'

1300 L3XI0-'

lOS maxwells 10< gauss

amp/m

3 X 10'

10- 3 gauss

kg m 3/amp' sec 3 = =ohm m amp' sec'ikg m 3 =fd'm

:0-

4. Magnetic units

Magnet isalion

Magnetic field inten- ampere per meter, sity . _ . . amp/m Inductance . henry, henry Permeability

henry per meter, henry/m

1

kg m 'amp'2 sec 2

10- 3 oersted

3 X 10'

amp/m 2

= ohm sec henry/tn

=

1/9 X 10-

11

1/9 X 10'3

'tl 'tl trl

Z

SZ m (J)

()

10-' em 10'

5. Optical units

Radiant flux

Luminance.

Jliuminance

. [ lumen. lumen . candela per square meter, candelajm 2 . lux, lux

candela steradian candela/m::

I

lumen-lrn:!

Note. The conversion factors given In the table tefer to the unrationaliseJ systems.

o""

00

.JJ

f SUBJECT INDEX Absorptive power (or absorptivity) of a body 169 Acceleration of free fall (tabulated data) 32 _ - uniform rotation, total 19 _ - uniformly accelerated rotation 16 ___ angular 18 ___ centripetal 19 - , tangential 18 Allowed current-carrying capacity of insulated wires 119 _ energy levels 115 Alloys of high ohmic resistance 119 Ampere 107, 133 Ampere-turns 136 Amplitude of wave 80 Angle, aperture 164 of incidence 159 - reflection 159 _ - , critical 175 - refraction 159 _ total reflection 159 _, polarisation 166 Artificially produced elements 195 Atomic unit of mass 186 Band, conduction 115 _, valence 115 Barriel-Iayer effect 168

Black body 168 Breakdown 114 Breaking stress (or ultimatE:: stress) 41, 42 Bulk elasticity 45 Caloric 52 Cal ori metrv 52 Candela 158 Candle, international 158 Capacitance 98 Ca paci tor 98 - , cylindrical 98 _, parallel plate 98 -, spherical 98 Centimeter (unit of capacitance) 98 Centre of gravity 36, 39 Change of vol ume upon mel ting 62 Charge, elementary 95, 186 -, negative 94 - , positive 94 Circuit, oscillating 151 Coefficient of friction 27, 34 internal friction 47 light, reflection 159 linear expansion 55, 68 _ _ pressure change at constant volume 57, 71 _ - resistivity, temperature 108 sound, absorption 93 - waves, reflectioll 93

r

208

SUBJECT INDEX

surface tension 56 - - volume expansion 55, 57, 67 Coerci ve force 141 Compressibility, isothermal 81 - of matter 41, 44 Conduction 56 - of a steady flow of liquid 46 Conductivity 108 -, electronic 146 , hole 116 -, induced 113 - , intrinsic 113 -, thermal 56, 70, 71 c.onstant of gravitation 27 - , Planck's 18 -, restoring force 76 Constants, emission 128 -, optical 160, 176 -, universal physical 203 Convection 55 Coulomb 94 Current, alternating 147 -, direct !06 -, induced !37 - of photoelectric cell, dark 168 - , pulsating direct 147 - , saturation 114 Currents, vortical fie! d of 134 - , eddy 139 Curve, magnetisation 140 brightness sensiof tivity 157 Deficit of nucleus, mass 189 Deformation 40 by tension (by cOIJ;pression) 40 -, elastic 40 Density 24 - . critical 54

IiIWiii-_
iiin

SUBJECT INDEX

- , current 107 - , energy 99 - of liquid and vapour, equilibrium 65, 66 - - substance 24, 29-32 - - various substances 32 Depth of penetration of high frequency currents 151 Diamagnetics 140 Diameters of molecules 72 Dielectric constant 103 - of medi um 94 Difference, potential 97 Diffraction 163 - grating 163 Diopter 162 Dipole, electric 100 -, moment of electric 100 Dispersion of the index of refraction 165 - - light velocity 165 - - velocity 80 Domain 141 Dynamics 22 - of fluids and gases 45 - - rotation 25

Emissive power (or emissivity) of a body 169 Energy of elastic deformation, potential 42 - level 187 - levels of the hydrogen atom 187, 191 - of motion (kinetic ener· gy) 24 -- - nucleous, binding 189 - - position (potential energy) 24 - - system 24 Epoch angle 76 Equation of adiabat 58 - , Bernoulli's 47 - , C!apeyron-Mendeleyev's 57 - , Einstein's 167 - of sine waves 80 Equilibrium, dynamic 54 - , neutral 36 - on an inclined plane 36 - , stable 36 , unstable 36 Equipotential surface 97 Error of measurement, absolute 201 - - - , mean absolute 201 - - - , relative 201

Effective val ue of al ternating current 148 Elastic I·imit 41 Electric circuit 107 - field 94 - -, intensity of 95 Electrochemical cell 113 - equivalent 112, 123 Electrolysis 112 Electrol ytes III Electromagnetic waves 153 El ectrol11agnetism 131 Electromotive force of electrochemical cells 124 --- - - a source 107 Electron-volt 113, 186 Electrostatic field 95 Emission constants 114

Factor, power 19 Fall of bodies, free 17 Farad 96 Ferroelectric crystals 104 Ferroelectrics (seignetteelectrics) 100 Ferromagnetics 140 Field, direction of magnetic 132 - intensity, magnetic 132, 134 - , magnetic 132 - of the earth, wagnetic 141

IIIIIiI

209

First law, Newton's 22 Fluid, ideal 46 Flux, luminous 157 - of radiation 157 Focal length of the lens 160 Force 22 . centripetal 26 - , Lorentz' 133 - , magnetic 131 of a magnetic field, line of 134 - - friction 27 Formula of thin lens 160 - , Stokes' 47 - , Thomson's 152 Frequency, cyclic 76 Friction, dry 27 - , rolling '27 - , sliding 27 Gap, forbidden 115 Gas laws 57 Gauss 134 Grating interval 163 Half life 190 Heat 51 of fusion 53, 61 - - vaporisation 53, 65 Heats of combustion of fuels 73 Henry 138 Humidity, absolute 60 - , maximum 60 - , relative 60, 74 Hysteresis 140 Illuminance 158, 173 Impedance 148 I m pulse 2:3 Index of refraction 177, 178 - -- - , absolute 159 - - - , relative 159 1ndudioll, electromagnetic 137

.....iiiiiiiii;;;;;;;;;;;;;;:===---- J5l

1"! 210

-, magnetic 132 Inertia 22, 23 Infrasonic vibrations 79 Instrument, the least separation for resolution of optical 164 -, ootical 160 Insulating materials 102 Intensity, luminous 157 - of radiation 157 -, sound 83, 92 Interaction of charges 94 Interference 162 Ionisation of gases 113 - potential 113, 127 Ions 112 Isotopes 188, 194, 195 Joule 110 Kilocalorie 52 Kinematics 15 Kinetic theory of gases 58 Law, Biot-Savart's 135 , Boyle's 157 _, Brewster's 166 -, Charles' 57 _, Gay-Lussac's (the equation of an isobaric process) 57 , Hooke's 40 - , Kirchhoff's, 169 -, Lenz' 137 -, Ohm's 108 _ of Kirchhoff and Bunsen 171 _ - universal gravitation 27 _, Stefan-Boltzmann's 169 Laws of the external photoelectric effect 167 _, Faraday's 112 -, Kirchhofi's 110 Lever 36

11'_ _.-...

SUBJECT INDEX

SUBJECT INDEX

Light, natural 165 - sources (tabulated data) 182 Line, Fraunhofer 171, 176, 177 - of force 96 Loop, hysteresis 140, 146 Loudness of sound 79, 80 Lumen 156 Luminance 158 - of illuminated surfaces 172 - - light sources 172 Lux 158 Magnetic equator 141 flux 136 - induction, residual 140 - materials 139 - pole 141 - saturation 141 - susceptibility 139 - -, specific 145 Magnetisation vector 139 Magnification of magnifying glass 160 - -- microscope 162 - - telescope 162 Mass number 188 - of body 23 Maxwell 137 Mean free path 60 Mechanics IS Meter 15 Mobility of electrons 126 - - ions 112, 126, 127 Model of atom, RutherfordBohr 186 Moduli of elasticity (table) 43 Modulus of volume elasticity (or bulk modulus) 42 - , shear 41 -, Young's 40 Molecular physics 51

_

Moment of force (or torque) 25 - - inertia 26 Moments of inertia of homogeneous bodies 33 Momentum 23 Motion, accelerated 17 - , amplitude of harmonic 75 curvilinear 16 , decelerated 17 -, harmonic 75 -, mechanical IS -, non-uniform 16 - of bodies in the earth's gravitational field 19 - body, rotational 17 - ideal fluid 46 - - point, circular 17 - - viscouse fluid 47 phase of harmonic 75 rectilinear 16 rotational 17 uniform 16 uniformly accelerated 16 , vibrational or oscillatory 75 Neutron 188 Nucleon 188 Number, Avogadro's 57 - , Faraday's 112 Oersted 134 Ohm 108 Optics 157 - , geometrical 159 Orbit, stationary 187 Oscillation, period of 75 Oscillations, angular frequency of dam ped 78 , forced 79 -, damped 78 , damping constant of damped 78

211

- , electric lSI - , free 78 - , initial amplitude of damped 78 - , instantaneous value of the amplitude of damped 78 - , mechanical 75 -, periodic 75 - , phase difference of 76 Oxide cathodes 114 Para magnetics 140 Parameters, critical 66 Particles, elementary and non-elementary 196 , energy of elementary and non-elementary 197 Pendulum 77 -, mathematical 77 -, physical 77 - , torsional 77 Perfect absorber 168 Period of natural oscillations lSI Permeability 144 - , initial 141 - of medi um 132 Phase of wave 80 Phat 158 Photoconductive cell 168, 184 Photoelectric cell 168, 183, 185 - effect 167 - -, external 167 - - , internal 167 Photometry 157 Photon 166 Piezoelectric constant 101, 106 - effect 101 Pitch of screw 38 sound 79 Plane of polarisation 166

SUBJECT INDEX

212

_, inductive 148 Reaction, thermonuclear 190 _, nuclear 190, 198, 199 Reflection, diffuse 160, 180 - of light 173, 174 - , total 159 Relative brightness sensitivity 171 Resistance (ohmic) 148 - of medium 47 Resistivity of electrolytes 120 _ - metals 117 Resonance 79 - , electric 52 - , series 149 Restoring force 76 Roentgen 199 Rotation of the plane of polarisation 166, 180 - , uniform 17 _, uniformly accelerated 18

l?oint, boiling 53, 61 -

maS5 ~5

-, melting 52 _, yield 41 poise 47 Polarisation 100 - of light 165 P.ower 24 _, optical 162 Votential, absolute normal 113, 123 _, electrochemical 113 _ gradient 98 Precision 200 Pressure 45 -, critical 5'1 _, partial 59 _, radiation 166 Principle, Archimedes' 46 _, Pascal's 45 Properties of ferrites, principal 144 _ _ light, quantum (cor puscular) 167 _ _ _ , wave 162 _ _ materials, magnetic 142, 143 _ _ saturated water va pour 67 _ _ semiconductors 129 Pulley block 38 -, fixed 37 _, movable 37 o

"

o

Quantum 188 _, energy of 197 _, radiation 166 !Radiation, thermal 168 Radioactivity 190 _, artificial 190 Ratio of photoconductive cell 168 _, Poisson's 41, 43 Reactance, capacitive 148

Scale, centigrade (Celsius) 51 _, Fahrenheit 51 - , Reaumur 51 Screw 38 Second 15 Second law, Newton's 23, 25 Self-inductance 138 Self-induction 137 Semiconductors 115 Sensitivity of the eye, relative brightness 157 _ _ photoconductive cell, s peci fie 168 _ _ photoelectric cell, integral 168 Series, the Balmer 191 - , - Lyman 191 _, - Paschen 191 Shear 41 - , absolute 41

SUBJECT INDEX

- , relative (shearing strain) 41 Shell, electron 189 Skin effect (or surface effect) 149 Sound 79 - pressure 83, 92 Source, current (electric generator) 107 Sources of waves, coherent 162 Spark gap 115, 131 Specific gravity 24 - heat 61, 63, 64 at constant pressure 52 - - - - volume 52 - - , mean (or average) 52, 62 - - , true 52, 62 Spectral emissivity 169 s.pectrum 169 - ,absorption 171 , continuous 170 - , electromagnetic IE3 - , emission 171, 181 - , line 170 - of mechanical vibrations 88, 89 - - radiation 169 -, sound frequency 87 Standard atmosphere 60, 72 Statics of liquids and gases 45 - - solid bodies 35 Stilb 156 Strain, longitudinal 40 - , transverse 41 Stress, allowed 45 - of deformation 40 Superconductivity 109 Superconductors, transition temperature of 118 Surface tension 68, 69 System of bodies, closed 23

21S

-

- elements, periodic 192-193 Systems of units, CGSE CGSM and MKSA 133: 204-205 Temperature of bod v 51 - coefficient of metals 117 - , cri tical 54 - , Curie (Curie point) 140 145 ' Theorem, Torricelli's 47 Theory of elasticity 40 Thermal electromotive force 116, 121, 122, 131 - expansion of solids and liquids 54 The,"mionic emission 114 Thermoelectricity 116 Tbird law, Newton's 23 Threshold of audibility 83 - - feeling 83 • - , photoelectric 167, 182 Torque (or moment of force) 25 Torsional rigidity 78 Trajectory 16 Transfer of heat 55 Types of spectra 169 Ul timate stress (or breaking stress) 41, 42 UI trasonic vibrations 79 Units of acceleration 17 - - measure of physica' quantities 202, 203 - - velocity 16 Vapour, saturated 54 Velocity, average angular IS - , esca pc 20, 22, 72 , instantaneous angular 18 - of electromagnetic waves 153

214

SUBJECT INDEX

molecules, average 59 - , the most probable 59 - , root mean square 58 non-uniform motion, average 16 - - rotational motion, linear 18 - seismic waves 86 - - sound 84, 85, 86 - - uniform motion 16 - - - rotation, angular 17 - - vibration 80 - - waves 80, 90 Viscosity 47, 48-50 Volt 97 Wave 79 - . cylindrical 80

intensity of 83 linearly polarised 166 longitudinal 81 plane 80 sine 80 spherical 80 , transverse 81 Wavelength 80 - of particle 191 Wavelengths of ultraviolet region of spectrum 174 - - visible region of spectrum 174 Weber 134, 137 Weight of body 36 Windlass 37 Work 24 - function 114 - of current-carrying wire in magnetic fielcj., 136