A Textbook of Engineering Physics_M. N. Avadhanulu, And P. G. Kshirsagar

5/21/2018 A Textbook of Engineering Physics_M. N. Avadhanulu, And P. G. Kshirsagar

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Scilab Textbook Companion for

A Textbook Of Engineering Physics

by M. N. Avadhanulu, And P. G. Kshirsagar1

Created byJumana Mp

btechElectronics Engineering

VNIT NAGPURCollege Teacher

Dr.A.S.GandhiCross-Checked by

Mukul R. Kulkarni

August 10, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the Textbook Companion Projectsection at the website http://scilab.in


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Book Description

Title: A Textbook Of Engineering Physics

Author: M. N. Avadhanulu, And P. G. Kshirsagar

Publisher: S. Chand And Company, New Delhi

Edition: 9

Year: 2011

ISBN: 81-219-0817-5

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 5

4 Electron Ballistics 9

5 Electron Optics 14

6 Properties of Light 17

7 Interference and Diffraction 19

8 Polarization 22

11 Architectural Acoustics 24

12 Ultrasonics 27

13 Atomic Physics 29

14 Lasers 36

15 Atomic nucleus and nuclear energy 39

16 Structure of Solids 49

17 The Band Theory of Solids 52

18 Semiconductors 54

19 PN Junction Diode 59

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21 Magnetic Materials 61

22 Superconductivity 64

23 Dielectrics 66

24 Fibre optics 71

25 Digital electronics 76

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List of Scilab Codes

Exa 4.1 Calculation of acceleration time taken and distance cov-ered and kinetic energy of an accelerating proton . . . 9

Exa 4.2 electrostatic deflection . . . . . . . . . . . . . . . . . . 10Exa 4.3 electron projected at an angle into a uniform electric field 10Exa 4.4 motion of an electron in a uniform magnetic field . . . 11Exa 4.5 motion of an electron in a uniform magnetic field acting

at an angle . . . . . . . . . . . . . . . . . . . . . . . . 11Exa 4.6 Magnetostatic deflection . . . . . . . . . . . . . . . . . 12Exa 4.7 electric and magnetic fields in crossed configuration. . 12Exa 5.1 Electron refraction calculation of potential difference . 14Exa 5.2 Cyclotron . . . . . . . . . . . . . . . . . . . . . . . . . 14Exa 5.4 calculation of linear separation of lines formed on pho-

tographic plates . . . . . . . . . . . . . . . . . . . . . 15

Exa 6.1 Optical path calculation . . . . . . . . . . . . . . . . . 17Exa 6.2 Coherence length calculation . . . . . . . . . . . . . . 17Exa 7.1 plane parallel thin film. . . . . . . . . . . . . . . . . . 19Exa 7.2 wedge shaped thin film . . . . . . . . . . . . . . . . . 19Exa 7.3 Newtons ring experiment . . . . . . . . . . . . . . . . 20Exa 7.4 nonreflecting film. . . . . . . . . . . . . . . . . . . . . 20Exa 8.2 Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . 22Exa 8.3 calculation of birefringence . . . . . . . . . . . . . . . 22Exa 11.1 calculation of total absorption and average absorption

coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 24Exa 11.2 calculation of average absorption coefficient . . . . . . 24Exa 11.3 calculation of average absorption coefficient and area . 25Exa 12.1 calculation of natural frequency. . . . . . . . . . . . . 27Exa 12.2 calculation of natural frequency. . . . . . . . . . . . . 27Exa 12.3 calculation of depth and wavelength . . . . . . . . . . 28

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Exa 13.1 calculation of rate of flow of photons . . . . . . . . . . 29

Exa 13.2 calculation of threshold wavelength and stopping poten-tial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Exa 13.3 calculation of momentum of Xray photon undergoing

scattering . . . . . . . . . . . . . . . . . . . . . . . . . 30Exa 13.4 calculation of wavelength of scattered radiation and ve-

locity of recoiled electrone . . . . . . . . . . . . . . . . 31Exa 13.5 calculation of wavelength of light emitted . . . . . . . 32Exa 13.6 calculation of de Broglie wavelength . . . . . . . . . . 32Exa 13.7 calculation of uncertainty in position . . . . . . . . . . 33Exa 13.8 Energy states of an electron and grain of dust . . . . . 34Exa 14.1 calculation of intensity of laser beam . . . . . . . . . . 36

Exa 14.2 calculation of intensity of laser beam . . . . . . . . . . 36Exa 14.3 calculation of coherence length bandwidth and line width 37Exa 14.4 calculation of frequency difference . . . . . . . . . . . 38Exa 14.5 calculation of frequency difference . . . . . . . . . . . 38Exa 15.1 calculation of binding energy per nucleon . . . . . . . 39Exa 15.2 calculation of energy . . . . . . . . . . . . . . . . . . . 39Exa 15.3 calculation of binding energy . . . . . . . . . . . . . . 40Exa 15.4 calculation of binding energy . . . . . . . . . . . . . . 41Exa 15.5 calculation of halflife . . . . . . . . . . . . . . . . . . . 41Exa 15.6 calculation of activity . . . . . . . . . . . . . . . . . . 42

Exa 15.7 calculation of age of mineral. . . . . . . . . . . . . . . 42Exa 15.8 calculation of age of wooden piece . . . . . . . . . . . 43Exa 15.9 calculation of energy released . . . . . . . . . . . . . . 44Exa 15.10 calculation of crossection . . . . . . . . . . . . . . . . 44Exa 15.11 calculation of final energy . . . . . . . . . . . . . . . . 45Exa 15.12 calculation of amount of fuel . . . . . . . . . . . . . . 45Exa 15.13 calculation of power output . . . . . . . . . . . . . . . 46Exa 15.14 calculation of power developed . . . . . . . . . . . . . 47Exa 15.15 calculation of amount of dueterium consumed . . . . . 47Exa 16.1 calculation of density . . . . . . . . . . . . . . . . . . 49Exa 16.2 calculation of no of atoms . . . . . . . . . . . . . . . . 49

Exa 16.3 calculation of distance . . . . . . . . . . . . . . . . . . 50Exa 16.4 calculation of interatomic spacing. . . . . . . . . . . . 51Exa 17.1 calculation of velocity of fraction of free electrone . . . 52Exa 17.2 calculation of velocity of e . . . . . . . . . . . . . . . . 52Exa 17.3 calculation of velocity of fraction of free electrones . . 53

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Exa 18.2 calculation of probability . . . . . . . . . . . . . . . . 54

Exa 18.3 calculation of fraction of e in CB . . . . . . . . . . . . 54Exa 18.4 calculation of fractionional change in no of e. . . . . . 55Exa 18.5 calculation of resistivity . . . . . . . . . . . . . . . . . 56Exa 18.6 calculation of conductivity of intrinsic and doped semi-

conductors . . . . . . . . . . . . . . . . . . . . . . . . 56Exa 18.7 calculation of hole concentration . . . . . . . . . . . . 57Exa 18.8 calculation of Hall voltage . . . . . . . . . . . . . . . . 57Exa 19.1 calculation of potential barrier . . . . . . . . . . . . . 59Exa 19.2 calculation of current . . . . . . . . . . . . . . . . . . 59Exa 21.1 calculation of magnetizing force and relative permeability 61Exa 21.2 calculation of magnetization and magnetic flux density 61

Exa 21.3 calculation of relative permeability . . . . . . . . . . . 62Exa 22.1 calculation of magnetic field. . . . . . . . . . . . . . . 64Exa 22.2 calculation of transition temperature . . . . . . . . . . 64Exa 22.3 calculation of temp at which there is max critical field 65Exa 23.1 calculation of relative permittivity . . . . . . . . . . . 66Exa 23.2 calculation of electronic polarizability . . . . . . . . . 66Exa 23.3 calculation of electronic polarizability and relative per-

mittivity . . . . . . . . . . . . . . . . . . . . . . . . . 67Exa 23.4 calculation of electronic polarizability and relative per-

mittivity . . . . . . . . . . . . . . . . . . . . . . . . . 68

Exa 23.5 calculation of ionic polarizability . . . . . . . . . . . . 68Exa 23.6 calculation of frequency and phase difference . . . . . 69Exa 23.7 calculation of frequency . . . . . . . . . . . . . . . . . 69Exa 24.1 Fiber optics numerical aperture calculation . . . . . . 71Exa 24.2 calculation of acceptance angle . . . . . . . . . . . . . 72Exa 24.3 calculation of normailsed frequency. . . . . . . . . . . 72Exa 24.4 calculation of normailsed frequency and no of modes . 73Exa 24.5 calculation of numerical aperture and maximum accep-

tance angle . . . . . . . . . . . . . . . . . . . . . . . . 73Exa 24.6 calculation of power level . . . . . . . . . . . . . . . . 74Exa 24.7 calculation of power loss . . . . . . . . . . . . . . . . . 74

Exa 25.1 sum of two binary numbers . . . . . . . . . . . . . . . 76Exa 25.2 sum of two binary numbers . . . . . . . . . . . . . . . 77Exa 25.3 sum of two binary numbers . . . . . . . . . . . . . . . 77Exa 25.4 difference of two binary numbers . . . . . . . . . . . . 78Exa 25.5 difference of two binary numbers . . . . . . . . . . . . 78

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Exa 25.6 difference of two binary numbers . . . . . . . . . . . . 79

Exa 25.7 product of two binary numbers . . . . . . . . . . . . . 80Exa 25.8 binary multiplication. . . . . . . . . . . . . . . . . . . 80Exa 25.9 binary division . . . . . . . . . . . . . . . . . . . . . . 81Exa 25.10 binary division . . . . . . . . . . . . . . . . . . . . . . 82Exa 25.11 octal addition. . . . . . . . . . . . . . . . . . . . . . . 82Exa 25.12 octal multiplication . . . . . . . . . . . . . . . . . . . 83Exa 25.13 hexadecimal addition . . . . . . . . . . . . . . . . . . 83Exa 25.14 binary to decimal conversion . . . . . . . . . . . . . . 84Exa 25.15 decimal to binary conversion . . . . . . . . . . . . . . 85Exa 25.16 decimal to binary conversion . . . . . . . . . . . . . . 85Exa 25.17 decimal to octal conversion . . . . . . . . . . . . . . . 87

Exa 25.18 octal to binary conversion . . . . . . . . . . . . . . . . 88Exa 25.19 octal to binary conversion . . . . . . . . . . . . . . . . 88Exa 25.20 binary to octal conversion . . . . . . . . . . . . . . . . 91Exa 25.21 hexa to decimal conversion . . . . . . . . . . . . . . . 94Exa 25.22 decimal to hexadecimal conversion . . . . . . . . . . . 94Exa 25.23 hexa to binary conversion . . . . . . . . . . . . . . . . 95Exa 25.24 binary to hexa conversion . . . . . . . . . . . . . . . . 96Exa 25.25 Substraction by ones complement method . . . . . . . 96Exa 25.26 Substraction by ones complement method . . . . . . . 99Exa 25.27 Substraction by ones complement method . . . . . . . 101

Exa 25.28 finding twos complement . . . . . . . . . . . . . . . . 104Exa 25.29 Addition of negative number by twos complement method 105Exa 25.30 Substraction by twos complement method . . . . . . . 108AP 1 Binary to Decimal convertor . . . . . . . . . . . . . . 112AP 2 Decimal to Base 2 Converter . . . . . . . . . . . . . . 114

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Chapter 4

Electron Ballistics

Scilab code Exa 4.1 Calculation of acceleration time taken and distancecovered and kinetic energy of an accelerating proton

1 clc ; clear ;

2 / / E xa mp le 4 . 13 / / C a l c u l a t i o n o f a c c e l e r a t i o n , t im e t ak en , d i s t a n c e

c ov er ed and k i n e t i c e n er gy o f an a c c e l e r a t i n gp r o t o n

4

5 / / g i v e n v a l u e s6 m = 1 . 6 7 * 1 0 ^ - 2 7 ; // mass o f p ro to n i n kg7 q = 1 . 6 0 2 * 1 0 ^ - 1 9 ; / / c h a r g e o f p r o t on i n Coulomb8 v 1 = 0 ; / / i n i t i a l v e l o c i t y i n m/ s9 v 2 = 2 . 5 * 1 0 ^ 6 ; // f i n a l v e l o c i t y i n m/ s

10 E = 5 0 0 ; // e l e c t r i c f i e l d st r e ng t h i n V/m11 // c a l c u l a t i o n12 a = E * q / m ; // a c c e l e r a t i o n13 disp (a , a c c e l e r a t i o n o f p ro to n i n (m/ s 2) i s : ) ;

14 t = v 2 / a ; / / t i m e15 disp (t , t im e ( i n s ) t ak e n by p r ot o n t o r e a ch t h e

f i n a l v e l o c i t y i s : ) ;16 x = a * t ^ 2 / 2 ; / / d i s t a n c e17 disp (x , d i s t a n c e ( i n m) c o ve re d by p ro to n i n t h i s

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t im e i s : ) ;

18 K E = E * q * x ; // k i n e t i c e ne rg y19 disp ( K E , k i n e t i c e ne rg y ( i n J ) a t t he t im e i s : ) ;

Scilab code Exa 4.2 electrostatic deflection

1 clc ; clear ;

2 / / E xa mp le 4 . 23 // e l e c t r o s t a t i c d e f l e c t i o n

4 / / g i v e n v a l u e s5 V 1 = 2 0 0 0 ; // i n v o l t s , p o t e n t i a l d i f f e r e n c e t hr ou ghwhi ch e l e c t r o n beam i s a c c e l e r a t e d

6 l = . 0 4 ; // l e ng t h o f r e c t a ng u l a r p l a t e s7 d = . 0 1 5 ; // d i s t a n c e b et we en p l a t e s8 V = 5 0 ; // p o t e n t i a l d i f f e r e n c e be t we en p l a t e s9 // c a l c u l a t i o n s

10 a l p h a = atan ( l * V / ( 2 * d * V 1 ) ) * ( 1 8 0 / % p i ) ; / / i n d e g r e e s11 disp ( a l p h a , a ng l e o f d e f l e c t i o n o f e l e c t r o n beam i s :

) ;12 v = 5 . 9 3 * 1 0 ^ 5 * sqrt ( V 1 ) ; // h o r i z o n t a l v e l o c i t y i n m/ s

13 t = l / v ; / / i n s14 disp (t , t r a n s i t t i m e t h r o u g h e l e c t r i c f i e l d i s : )

Scilab code Exa 4.3 electron projected at an angle into a uniform electricfield

1 clc ; clear ;

2 / / E xa mp le 4 . 3

3 / / e l e c t r o n p r o j e c t e d a t an a n gl e i n t o a u ni fo rme l e c t r i c f i e l d

4 / / g i v e n v a l u e s5 v 1 = 4 . 5 * 1 0 ^ 5 ; // i n i t i a l spe e d i n m/ s6 a l p h a = 3 7 * % p i / 1 8 0 ; // a ng l e o f p r o j e c t i o n i n d e g r e e s

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7 E = 2 0 0 ; / / e l e c t r i c f i e l d i n t e n s i t y i n N/C

8 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C9 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g10 a = e * E / m ; // a c c e l e r a t i o n i n m/ s 211 t = 2 * v 1 * sin ( a l p h a ) / a ; // t im e i n s12 disp (t , t i m e t a ke n by e l e c t r o n t o r e t u r n t o i t s

i n i t i a l l e v e l i s : )13 H = ( v 1 ^ 2 * sin ( a l p h a ) * sin ( a l p h a ) ) / ( 2 * a ) ; // h e i g h t i n m14 disp (H , maximum h e i g h t r e a ch e d by e l e c t r o n i s : )15 s = ( v 1 ^ 2 ) * ( 2 * sin ( a l p h a ) * cos ( a l p h a ) ) / ( 2 * a ) ; //

d i s pl a c em e n t i n m16 disp (s , h o r i z o n t a l d i s p l a c e me n t ( i n m) when i t r e a c h e s

maximum h e i g h t i s : )

Scilab code Exa 4.4 motion of an electron in a uniform magnetic field

1 clc ; clear ;

2 / / E xa mp le 4 . 43 // m ot io n o f an e l e c t r o n i n a u ni fo rm m ag ne ti c f i e l d4 / / g i v e n v a l u e s5 V = 2 0 0 ; // p o t e n t i a l d i f f e r e n c e t hr ou gh whi ch e l e c t r o n

i s a c c e l e r a t e d i n v o l t s6 B = 0 . 0 1 ; / / m a g n e t i c f i e l d i n wb /m 27 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C8 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g9 v = sqrt ( 2 * e * V / m ) ; // e l e c t r o n v e l o c i t y i n m/ s

10 disp (v , e l e c t r o n v e l o c i t y i s : )11 r = m * v / ( e * B ) ; / / i n m12 disp (r , r a d i u s o f p at h ( i n m) i s : )

Scilab code Exa 4.5 motion of an electron in a uniform magnetic fieldacting at an angle

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1 clc ; clear ;

2 / / E xa mp le 4 . 53 // m ot io n o f an e l e c t r o n i n a u ni fo rm m ag ne ti c f i e l da c ti n g a t a n a ng l e

4 / / g i v e n v a l u e s5 v = 3 * 1 0 ^ 7 ; // e l e c t r o n s pe ed6 B = . 2 3 ; / / m a g n e t i c f i e l d i n wb /m 27 q = 4 5 * % p i / 1 8 0 ; // i n d e gr ee s , a n g le i n wh ich e l e c t r o n

e n t e r f i e l d8 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C9 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g

10 R = m * v * sin ( q ) / ( e * B ) ; / / i n m

11 disp (R , r a di u s o f h e l i c a l pat h i s : )12 p = 2 * % p i * m * v * cos ( q ) / ( e * B ) ; / / i n m13 disp (p , p i t ch o f h e l i c a l pa th ( i n m) i s : )

Scilab code Exa 4.6 Magnetostatic deflection

1 clc ; clear ;

2 / / E xa mp le 4 . 6

3 // M a gn e to s ta t i c d e f l e c t i o n4 / / g i v e n v a l u e s5 D = . 0 3 ; // d e f l e c t i o n i n m6 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g7 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C8 L = . 1 5 ; / / d i s t a n c e b et we en CRT a nd a no de i n m9 l = L / 2 ;

10 V = 2 0 0 0 ; // i n v o l t s i n wb/11 B = D * sqrt ( 2 * m * V ) / ( L * l * sqrt ( e ) ) ; // i n wb/m212 disp (B , t r a n s v e r s e m a g ne t ic f i e l d a c t i n g ( i n wb/m 2 )

i s : )

Scilab code Exa 4.7 electric and magnetic fields in crossed configuration

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1 clc ; clear ;

2 / / E xa mp le 4 . 73 / / e l e c t r i c a nd m a g n e t i c f i e l d s i n c r o s s e dc o n f i g u r a t i o n

4 / / g i v e n v a l u e s5 B = 2 * 1 0 ^ - 3 ; / / m a g n e t i c f i e l d i n wb /m 26 E = 3 . 4 * 1 0 ^ 4 ; // e l e c t r i c f i e l d i n V/m7 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g8 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C9 v = E / B ; // i n m/ s

10 disp (v , e l e c t r o n s pe ed i s : )11 R = m * v / ( e * B ) ; / / i n m

12 disp (R , r a d i u s o f c i r c u l a r p at h ( i n m) when e l e c t r i cf i e l d i s s w it c he d o f f )

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Chapter 5

Electron Optics

Scilab code Exa 5.1 Electron refraction calculation of potential difference

1 clc ; clear ;

2 / / E xa mp le 5 . 13 // E l e c t r o n r e f r a c t i o n , c a l c u l a t i o n o f p o t e n t i a l

d i f f e r e n c e4

5 / / g i v e n v a l u e s6 V 1 = 2 5 0 ; // p o t e n t i a l by which e l e c t r o n s a r e

a c c e l e r a t e d i n V ol ts7 a l p h a 1 = 5 0 * % p i / 1 8 0 ; / / i n d e g r e e8 a l p h a 2 = 3 0 * % p i / 1 8 0 ; / / i n d e g r e e9 b = sin ( a l p h a 1 ) / sin ( a l p h a 2 ) ;

10 // c a l c u l a t i o n11 V 2 = ( b ^ 2 ) * V 1 ;

12 a = V 2 - V 1 ;

13 disp (a , p o t e n t i a l d i f f e r e n c e ( i n v o l t s ) i s : ) ;

Scilab code Exa 5.2 Cyclotron

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1 clc ; clear ;

2 / / E xa mp le 5 . 2 & 5 . 33 / / C y cl ot ro n , c a l c u l a t i o n o f m ag ne ti c i n du c ti o n ,maximum en er gy

4

5 / / g i v e n v a l u e s6 f = 1 2 * ( 1 0 ^ 6 ) ; / / o s c i l l a t o r f r e q u e n c y i n H e r t z7 r = . 5 3 ; // r a d i u s o f t he d ee i n me t r e8 q = 1 . 6 * 1 0 ^ - 1 9 ; // D e ut er on c h a rg e i n C9 m = 3 . 3 4 * 1 0 ^ - 2 7 ; // mass o f d e ut er o n i n kg

10 // c a l c u l a t i o n11 B = 2 * % p i * f * m / q ; //

12 disp (B , m a gn et i c i n d u c t i o n ( i n T e sl a ) i s : ) ;13 E = B ^ 2 * q ^ 2 * r ^ 2 / ( 2 * m ) ;

14 disp (E , maximum e n e r g y t o w hi ch d e u t e r o n s c an b ea c c e l e r a t e d ( i n J ) i s )

15 E 1 = E * 6 . 2 4 * 1 0 ^ 1 8 / 1 0 ^ 6 ; / / c o n v e r s i o n o f e n er g y i n t o MeV16 disp ( E 1 , maximum e n e r g y t o w hi ch d e u t e r o n s c an b e

a c c e l e r a t e d ( i n MeV) i s ) ;

Scilab code Exa 5.4 calculation of linear separation of lines formed onphotographic plates

1 clc ; clear ;

2 / / E xa mp le 5 . 43 / /Mass s pe ct ro gr ap h , c a l c u l a t i o n o f l i n e a r

s e p a r at i o n o f l i n e s fo rmed o n p h ot og r ap hi c p l a t e s4

5 / / g i v e n v a l u e s6 E = 8 * 1 0 ^ 4 ; // e l e c t r i c f i e l d i n V/m

7 B = . 5 5 / / m a g n et i c i n d u c t i o n i n Wb/m28 q = 1 . 6 * 1 0 ^ - 1 9 ; // c ha r ge o f i o n s9 m 1 = 2 0 * 1 . 6 7 * 1 0 ^ - 2 7 ; // a t o mi c mass o f an i s o t o p e o f

neon10 m 2 = 2 2 * 1 . 6 7 * 1 0 ^ - 2 7 ; // a t o mi c m ass o f o t h e r i s o t o p e o f

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neon

11 // c a l c u l a t i o n12 x = 2 * E * ( m 2 - m 1 ) / ( q * B ^ 2 ) ; //13 disp (x , s e p a r a t i o n o f l i n e s ( i n me t r e ) i s : )

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Chapter 6

Properties of Light

Scilab code Exa 6.1 Optical path calculation

1 clc ; clear ;

2 / / E xa mp le 6 . 13 // O p t ic a l p ath c a l c u l a t i o n4

5 / / g i v e n v a l u e s6 n = 1 . 3 3 ; // r e f r a c t i v e i n de x o f medium7 x = . 7 5 ; / / g e o m e t r i c a l p at h i n m i cr o me tr e8 // c a l c u l a t i o n9 y = x * n ; //

10 disp (y , o p t i c a l p at h ( i n m ic ro me tr e ) i s : )

Scilab code Exa 6.2 Coherence length calculation

1 clc ; clear ;

2 / / E xa mp le 6 . 23 // C o he re nc e l e n g t h c a l c u l a t i o n4

5 / / g i v e n v a l u e s

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6 l = 1 * 1 0 ^ - 1 4 ; // l i n e w id th i n m et re

7 x = 1 0 . 6 * 1 0 ^ - 6 ; / /IR e m i s s i o n w a ve l en g th i n m et re8 // c a l c u l a t i o n9 y = x ^ 2 / l ; //

10 disp (y , c o h e r e n c e l e n g t h ( i n m et re ) i s : )

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Chapter 7

Interference and Diffraction

Scilab code Exa 7.1 plane parallel thin film

1 clc ; clear ;

2 / / E xa mp le 7 . 13 / / p la ne p a r a l l e l t hi n f i l m4

5 / / g i v e n v a l u e s6 x = 5 8 9 0 * 1 0 ^ - 1 0 ; // w av el en gt h o f l i g h t i n m etr e7 n = 1 . 5 ; // r e f r a c t i v e i nd ex8 r = 6 0 * % p i / 1 8 0 ; // a ng l e o f r e f r a c t i o n i n d eg r e e9 // c a l c u l a t i o n

10 t = x / ( 2 * n * cos ( r ) ) ;

11 disp ( t * 1 0 ^ 6 , t h i c k n e s s o f p l a t e ( i n m ic ro me tr e ) i s : ) ;

Scilab code Exa 7.2 wedge shaped thin film

1 clc ; clear ;

2 / / E xa mp le 7 . 23 / / wedge s ha pe d t h i n f i l m

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4

5 / / g i v e n v a l u e s6 x = 5 8 9 3 * 1 0 ^ - 1 0 ; // w av el en gt h o f l i g h t i n m etr e7 n = 1 . 5 ; // r e f r a c t i v e i nd ex8 y = . 1 * 1 0 ^ - 3 ; // f r i n g e s p a c in g9 // c a l c u l a t i o n

10 z = x / ( 2 * n * y ) ; / / a n g l e o f wed ge11 a l p h a = z * 1 8 0 / % p i ; // c o n ve r si o n o f r ad i an i n t o d e g r e e12 disp ( a l p h a , a n g l e o f wedg e ( i n d e g r e e ) i s : ) ;

Scilab code Exa 7.3 Newtons ring experiment

1 clc ; clear ;

2 / / E xa mp le 7 . 33 / / Newto n s r i n g e x p e r i m e n t c a l c u l a t i o n o f

r e f r a c t i v e i nd ex4

5 / / g i v e n v a l u e s6 D 1 = 1 . 5 ; // d i am et re ( i n cm ) o f t en t h d ar k r i n g i n a i r7 D 2 = 1 . 2 7 ; / / d i a me t r e ( i n cm ) o f t e n th d ar k r i n g i n

l i q u i d8

9

10 // c a l c u l a t i o n11 n = D 1 ^ 2 / D 2 ^ 2 ;

12 disp (n , r e f r a c t i v e i n d e x o f l i q u i d i s ) ;

Scilab code Exa 7.4 nonreflecting film

1 clc ; clear ;

2 / / E xa mp le 7 . 43 // n o n r e f l e c t i n g f i l m4

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6 l = 5 5 0 0 * 1 0 ^ - 1 0 ; // w av el en gt h o f l i g h t7 n 1 = 1 . 3 3 ; // r e f r a c t i v e i nd ex o f w a te r8 n 2 = 1 . 5 2 ; // r e f r a c t i v e i nd ex o f g l a s s window pane9 x = sqrt ( n 1 ) ; // t o c h e c k i f i t i s n o n r e f l e c t i n g

10

11 // c a l c u l a t i o n12 t = l / ( 4 * n 1 ) ; // t h i c k n e s s o f w at er f i l m r e q u i r e d13 disp ( t * 1 0 ^ 6 , minimum t h i c k n e s s o f f i l m ( i n m et re ) i s

) ;

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Chapter 8

Polarization

Scilab code Exa 8.2 Polarizer

1 clc ; clear ;

2 / / E xa mp le 8 . 23 // P o l a r i z e r , c a l c u l a t i o n o f a n gl e4

5 / / g i v e n v a l u e s6 I o = 1 ; // i n t e n s i t y o f p o l a r i s e d l i g h t7 I 1 = I o / 2 ; // i n t e n s i t y o f beam p o l a r i s e d by f i r s t by

f i r s t p o l a r i s e r8 I 2 = I o / 3 ; // i n t e n s i t y o f l i g h t p o l a r i s e d by s ec o nd

p o l a r i s e r9

10

11 // c a l c u l a t i o n12 a = acos ( sqrt ( I 2 / I 1 ) ) ;

13 a l p h a = a * 1 8 0 / % p i ; // c o n ve r si o n o f a n gl e i n t o d e g r ee14 disp ( a l p h a , a ng l e be t we en c h a r a c t e r i s t i c d i r e c t i o n s

( i n d e gr e e ) i s ) ;

Scilab code Exa 8.3 calculation of birefringence

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1 clc ; clear ;

2 / / E xa mp le 8 . 33 // c a l c u l a t i o n o f b i r e f r i n g e n c e4

5 / / g i v e n v a l u e s6

7 l = 6 * 1 0 ^ - 7 ; // w av el en gt h o f l i g h t i n m et re8 d = 3 * 1 0 ^ - 5 ; // t h i c k n e ss o f c r y s t a l9

10

11 // c a l c u l a t i o n12 x = l / ( 4 * d ) ;

13 disp (x , t h e b i r e f r i n g a n c e o f t h e c r y s t a l i s ) ;

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Chapter 11

Architectural Acoustics

Scilab code Exa 11.1 calculation of total absorption and average absorp-tion coefficient

1 clc ; clear ;

2 / / E x am pl e 1 1 . 13 / / c a l c u l a t i o n o f t o t a l a b s or p t i o n and a ve ra ge

ab so rp ti on c o e f f i c i e n t4

5 / / g i v e n v a l u e s6

7 V = 2 0 * 1 5 * 5 ; // v olume o f h a l l i n m38 t = 3 . 5 ; // r e v e r b e r a t i o n t im e o f empty h a l l i n s e c9

10

11 // c a l c u l a t i o n12 a 1 = . 1 6 1 * V / t ; // t o t a l a b s or p t i o n o f empty h a l l13 k = a 1 / ( 2 * ( 2 0 * 1 5 + 1 5 * 5 + 2 0 * 5 ) ) ;

14 disp (k , t h e a v e r a g e a b s o r p t i o n c o e f f i c i e n t i s ) ;

Scilab code Exa 11.2 calculation of average absorption coefficient

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1 clc ; clear ;

2 / / E x am pl e 1 1 . 23 / / c a l c u l a t i o n o f a v e r a g e a b s o r p t i o n c o e f f i c i e n t4

5 / / g i v e n v a l u e s6

7 V = 1 0 * 8 * 6 ; // v olume o f h a l l i n m38 t = 1 . 5 ; // r e v e r b e r a t i o n t im e o f empty h a l l i n s e c9 A = 2 0 ; // a r e a o f c u r t a i n c l o t h i n m2

10 t 1 = 1 ; // new r e v e r b e r a t i o n t im e i n s e c11

12 // c a l c u l a t i o n

13 a 1 = . 1 6 1 * V / t ; // t o t a l a b s or p t i o n o f empty h a l l14 a 2 = . 1 6 1 * V / t 1 ; // t o t a l a b so r p t i o n a f t e r a c u r t a i n

c l o t h i s s us pe nd ed15

16 k = ( a 2 - a 1 ) / ( 2 * 2 0 ) ;

17 disp (k , t h e a v e r a g e a b s o r p t i o n c o e f f i c i e n t i s ) ;

Scilab code Exa 11.3 calculation of average absorption coefficient and area

1 clc ; clear ;

2 / / E x am pl e 1 1 . 33 / / c a l c u l a t i o n o f a v e r a g e a b s o r p t i o n c o e f f i c i e n t and

a r e a4

5 / / g i v e n v a l u e s6

7 V = 2 0 * 1 5 * 1 0 ; // v olume o f h a l l i n m38 t = 3 . 5 ; // r e v e r b e r a t i o n t im e o f empty h a l l i n s e c

9 t 1 = 2 . 5 ; // r e du c ed r e v e r b e r a t i o n t im e10 k 2 = . 5 ; / / a b s o r p t i o n c o e f f i c i e n t o f c u r t a i n c l o t h11 // c a l c u l a t i o n12 a 1 = . 1 6 1 * V / t ; // t o t a l a b s or p t i o n o f empty h a l l13 k 1 = a 1 / ( 2 * ( 2 0 * 1 5 + 1 5 * 1 0 + 2 0 * 1 0 ) ) ;

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14 disp ( k 1 , t h e a v e r a g e a b s o r p t i o n c o e f f i c i e n t i s ) ;

15 a 2 = . 1 6 1 * V / t 1 ; // t o t a l a b s or p t i o n when w a ll i s c ov er edw it h c u r t a i n16 a = t 1 * ( a 2 - a 1 ) / ( t 1 * k 2 ) ;

17 disp (a , a re a o f w a ll t o be c ov er ed w i th c u r t a i n ( i n m 2 ) i s : )

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Chapter 12

Ultrasonics

Scilab code Exa 12.1 calculation of natural frequency

1 clc ; clear ;

2 / / E x am pl e 1 2 . 13 // c a l c u l a t i o n o f n a t u r a l f re qu e nc y , m a g n e t o s t r i c t i o n4

5 / / g i v e n v a l u e s6

7 l = 4 0 * 1 0 ^ - 3 ; // l e ng t h o f p ur e i r o n r od8 d = 7 . 2 5 * 1 0 ^ 3 ; // d e n s i t y o f i r o n i n kg /m39 Y = 1 1 5 * 1 0 ^ 9 ; //Young s modulus in N/m2

10

11 // c a l c u l a t i o n12 f = ( 1 * sqrt ( Y / d ) ) / ( 2 * l ) ;

13 disp ( f * 1 0 ^ - 3 , t h e n a t u r a l f r e q u e n cy ( i n kHz ) i s ) ;

Scilab code Exa 12.2 calculation of natural frequency

1 clc ; clear ;

2 / / E x am pl e 1 2 . 2

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3 / / c a l c u l a t i o n o f n a t ur a l f r eq u en c y

45 / / g i v e n v a l u e s6

7 t = 5 . 5 * 1 0 ^ - 3 ; // t h i c k n e s s i n m8 d = 2 . 6 5 * 1 0 ^ 3 ; / / d e n s i t y i n k g /m 39 Y = 8 * 1 0 ^ 1 0 ; //Young s modulus in N/m2

10

11

12 // c a l c u l a t i o n13 f =( sqrt ( Y / d ) ) / ( 2 * t ) ; // f r e qu e n cy i n h e r t z14 disp ( f * 1 0 ^ - 3 , t h e n a t u r a l f r e q u e n cy ( i n kHz ) i s ) ;

Scilab code Exa 12.3 calculation of depth and wavelength

1 clc ; clear ;

2 / / E x am pl e 1 2 . 33 // c a l c u l a t i o n o f d ep th and w av el en gt h4

5 / / g i v e n v a l u e s6

7 f = . 0 7 * 1 0 ^ 6 ; / / f r e q u e n c y i n Hz8 t = . 6 5 ; // t im e t a ke n f o r p u l s e t o r e t u r n9 v = 1 7 0 0 ; // v e l o c i t y o f sound i n s e a w at er i n m/ s

10

11 // c a l c u l a t i o n12 d = v * t / 2 ; //13 disp (d , t h e d ep th o f s e a ( i n m) i s ) ;14 l = v / f ; // w av el en gh t o f p u l s e i n m15 disp ( l * 1 0 ^ 2 , w a ve l en g th o f p u l s e ( i n cm ) i s ) ;

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Chapter 13

Atomic Physics

Scilab code Exa 13.1 calculation of rate of flow of photons

1 clc ; clear ;

2 / / E x am pl e 1 3 . 13 / / c a l c u l a t i o n o f r a t e o f f lo w o f p h ot o ns4

5 / / g i v e n v a l u e s6

7 l = 5 8 9 3 * 1 0 ^ - 1 0 ; // w av el en gt h o f l i g h t i n m8 P = 4 0 ; / / po wer o f s od iu m lamp i n W9 d = 1 0 ; // d i s t a n c e from t he s o ur c e i n m

10 s = 4 * % p i * d ^ 2 ; // s u r f a c e a r e a o f r a d i us i n m211 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s12 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s13 // c a l c u l a t i o n14 E = P * 1 ; //15 disp (E , t o t a l e n er g y e m i tt e d p e r s e co n d ( i n J o u l e ) i s

) ;

16 n = E * l / ( c * h ) ; // t o t a l no o f p ho to ns17 R = n / s ;

18 disp (R , r a t e o f f l o w o f p ho to ns p er u n it a re a ( i n /m 2) i s )

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Scilab code Exa 13.2 calculation of threshold wavelength and stoppingpotential

1 clc ; clear ;

2 / / E x am pl e 1 3 . 23 // c a l c u l a t i o n o f t h r e s h o l d w av el en gt h and s t op p in g

p o t e n t i a l4

5 / / g i v e n v a l u e s6

7 l = 2 0 0 0 ; // w av el en gt h o f l i g h t i n a rm st ro ng8 e = 1 . 6 * 1 0 ^ - 1 9 ; // c ha rg e o f e l e c t r o n9 W = 4 . 2 ; // work f u n c t i o n i n eV

10 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s11 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s12 // c a l c u l a t i o n13 x = 1 2 4 0 0 / ( W ) ; // h c = 12400 eV14 disp (x , t h r e s h o l d w a v e l e n g t h ( i n A rm s tr on g ) i s ) ;15 V s = ( 1 2 4 0 0 / l - W ) ; //

16 disp ( V s , s t o p p i n g p o t e n t i a l ( i n VOLTS ) i s )

Scilab code Exa 13.3 calculation of momentum of Xray photon undergo-ing scattering

1 clc ; clear ;

2 / / E x am pl e 1 3 . 33 / / c a l c u l a t i o n o f momentum o f Xr ay p ho to n u n d er g o in g

s c a t t e r i n g4

5 / / g i v e n v a l u e s6

7 a l p h a = 6 0 * % p i / 1 8 0 ; // s c a t t e r i n g a n gl e i n r ad i an

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8 e = 1 . 6 * 1 0 ^ - 1 9 ; // c h ar g e o f e l e c t r o n e

9 W = 1 2 2 7 3 ; // work f u n c t i o n i n eV10 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s11 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s12 h c = 1 2 4 0 0 ; // i n eV13 m = 9 . 1 * 1 0 ^ - 3 1 // r e st m a ss o f p ho to n i n kg14 // c a l c u l a t i o n15 x = h c / ( W ) ; / / w a v el e n g th o f p ho to n u n d e r g o i n g m o d of i ed

s c a t t e r i n g i n a rm st ro ng16 y = x - ( h / ( m * c ) ) * ( 1 - cos ( a l p h a ) ) ;

17 p = h / y * 1 0 ^ 1 0 ;

18 disp (p ,momentum o f photon ( in kgm/ s ) i s ) ;

Scilab code Exa 13.4 calculation of wavelength of scattered radiation andvelocity of recoiled electrone

1 clc ; clear ;

2 / / E x am pl e 1 3 . 43 // c a l c u l a t i o n o f w a ve l en gt h o f s c a t t e r e d r a d i a t i o n

and v e l o c i t y o f r e c o i l e d e l e c t r o n4

5 / / g i v e n v a l u e s6

7 a l p h a = 3 0 * % p i / 1 8 0 ; // s c a t t e r i n g a n gl e i n r ad i an8 e = 1 . 6 * 1 0 ^ - 1 9 ; // c h ar g e o f e l e c t r o n9 x = 1 . 3 7 2 * 1 0 ^ - 1 0 ; // w av el en gt h o f i n c i d e n t r a d i a t i o n i n

m10 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s11 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s12 m = 9 . 1 * 1 0 ^ - 3 1 // r e s t mass o f p ho to n i n kg

13 h c = 1 2 4 0 0 ; // i n eV14 // c a l c u l a t i o n15

16 y = ( ( x + ( h / ( m * c ) ) * ( 1 - cos ( a l p h a ) ) ) ) * 1 0 ^ 1 0 ;

17 disp (y , w av el en gt h o f s c a t t e r e d r a d i a t i o n ( i n

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a r m s t r o n g ) i s ) ;

18 x 1 = x * 1 0 ^ 1 0 ; // c o n v e r ti n g i n c i d e n t w av el en gt h i n t oa r m s t r o n g19 K E = h c * e * ( ( 1 / x 1 ) - ( 1 / y ) ) ; // k i n e t i c e ne rg y i n J ou l e20 disp ( K E , k i n e t i c e n e r g y i n j o u l e i s ) ;21 v = sqrt ( 2 * K E / m ) ;

22 disp (v , v e l o c i t y o f r e c o i l e d e l e c t r o n ( i n m/ s 2) i s );

Scilab code Exa 13.5 calculation of wavelength of light emitted

1 clc ; clear ;

2 / / E x am pl e 1 3 . 53 / / c a l c u l a t i o n o f w av el en gt h o f l i g h t e mi tt ed4

5 / / g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ; // c ha rg e o f e l e c t r o n e7 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t8 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s9 E 1 = 5 . 3 6 ; / / e n er g y o f f i r s t s t a t e i n eV

10 E 2 = 3 . 4 5 ; // e ne rg y o f s ec on d s t a t e i n eV11

12

13 // 1 ) c a l c u l a t i o n14

15 l = h * c * 1 0 ^ 1 0 / ( ( E 1 - E 2 ) * e ) ;

16 disp (l , w a ve l en g th o f s c a t t e r e d l i g h t ( i n A rm st ro ng )i s ) ;

Scilab code Exa 13.6 calculation of de Broglie wavelength

1 clc ; clear ;

2 / / E x am pl e 1 3 . 6

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3 // c a l c u l a t i o n o f de B r o g l i e w av el en gt h

45 / / 1 ) g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ;

7 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s8 V = 1 8 2 ; // p o t e n t i a l d i f f e r e n c e i n v o l t s9 m = 9 . 1 * 1 0 ^ - 3 1 ; // mass o f e i n kg

10

11

12 // 1 ) c a l c u l a t i o n13

14 l = h / sqrt ( 2 * e * m * V ) ;

15 disp (l , d e B r o g l i e w a v e l e n g t h ( i n m) i s ) ;16

17

18 / / 2 ) g i v e n v a l u e s19 m 1 = 1 ; // mass o f o b j e ct i n kg20 v = 1 ; // v e l o c i t y o f o b j e ct i n m/ s21 l 1 = h / ( m 1 * v ) ;

22 disp ( l 1 , d e br o g ie w av el en gt h o f o b j e c t i n m) i s ) ;

Scilab code Exa 13.7 calculation of uncertainty in position

1 clc ; clear ;

2 / / E x am pl e 1 3 . 73 / / c a l c u l a t i o n o f u n ce r ta i nt y i n p o s i t i o n4

5 / / 1 ) g i v e n v a l u e s6

7 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s

8 v 1 = 2 2 0 ; // v e l o c i t y o f e i n m/ s9 m = 9 . 1 * 1 0 ^ - 3 1 ; // mass o f e i n kg

10 A = 0 . 0 6 5 / 1 0 0 ; / / a c c u r a c y11

12

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13 // 1 ) c a l c u l a t i o n

14 v 2 = v 1 * A ; // u n c e r t a i n t y i n s pe ed15 x 1 = h / ( 2 * % p i * m * v 2 ) ; //16 disp ( x 1 , u n c er t a i n t y i n p o s i t i o n o f e ( i n m) i s ) ;17

18

19 / / 2 ) g i v e n v a l u e s20 m 1 = 1 5 0 / 1 0 0 0 ; // mass o f o b j e c t i n kg21 x 2 = h / ( 2 * % p i * m 1 * v 2 ) ;

22 disp ( x 2 , u n c er t a i n t y i n p o s i t i o n o f b a s e b a l l ( i n m)i s ) ;

Scilab code Exa 13.8 Energy states of an electron and grain of dust

1 clc ; clear ;

2 / / E x am pl e 1 3 . 83 / / c a l c u l a t i o n o f e n er gy s t a t e s o f an e l e c t r o n and

g r a i n o f d us t and c om pa ri ng4

5 / / 1 ) g i v e n v a l u e s6 L 1 = 1 0 * 1 0 ^ - 1 0 ; // w i dt h o f p o t e n t i a l w e l l i n whi ch e i s

c o n f i n e d7 L 2 = . 1 * 1 0 ^ - 3 ; // w i d t h o f p o t e n t i a l w e l l i n which g r a i n

o f d u s t i s c on f i n e d8 h = 6 . 6 2 6 * 1 0 ^ - 3 4 ; / / Pl an ck s c o n s t a n t i n J s9 v 1 = 1 0 ^ 6 ; // v e l o c i t y o f g a ri n o f d u st i n m/ s

10 m 1 = 9 . 1 * 1 0 ^ - 3 1 ; // mass o f e i n kg11 m 2 = 1 0 ^ - 9 ; // mass o f g r a i n i n kg12

13 // 1 ) c a l c u l a t i o n

1415 E e 1 = 1 ^ 2 * h ^ 2 / ( 8 * m 1 * L 1 ^ 2 ) ; // f i r s t e n er g y s t a t e o f

e l e c t r o n16 disp ( E e 1 , f i r s t e ne rg y s t a t e o f e i s ) ;17 E e 2 = 2 ^ 2 * h ^ 2 / ( 8 * m 1 * L 1 ^ 2 ) ; // s ec on d e ne rg y s t a t e o f

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e l e c t r o n

18 disp ( E e 2 , s e c o n d e n er g y s t a t e o f e i s ) ;19 E e 3 = 3 ^ 2 * h ^ 2 / ( 8 * m 1 * L 1 ^ 2 ) ; // t h i r d e ne rg y s t a t e o f e l e c t r o n

20 disp ( E e 3 , t hi r d e n e r g y s t a t e o f e i s ) ;21 disp ( E ne rg y l e v e l s o f an e l e c t r o n i n an i n f i n i t e

p o t e n t i a l w e l l a r e q u an t is e d a nd t he e ne rg yd i f f e r e n c e be t we en t h e s u c c e s s i v e l e v e l s i s q u i t e

l a r g e . E l e c tr o n c an no t jump fro m o ne l e v e l t oo t h e r on s t r e n g t h o f t h er m al e n er g y . Henceq u a n t i z a t i o n o f e n e r g y p l a y s a s i g n i f i c a n t r o l ei n c as e o f e l e c t r o n )

2223 E g 1 = 1 ^ 2 * h ^ 2 / ( 8 * m 2 * L 2 ^ 2 ) ; // f i r s t e n er g y s t a t e o f

g r a i n o f d u st24 disp ( E g 1 , f i r s t e ne rg y s t a t e o f g r a i n o f d us t i s ) ;25 E g 2 = 2 ^ 2 * h ^ 2 / ( 8 * m 2 * L 2 ^ 2 ) ; // s ec on d e ne rg y s t a t e o f

g r a i n o f d u st26 disp ( E g 2 , s e c o n d e n er g y s t a t e o f g r a i n o f d u s t i s )

;

27 E g 3 = 3 ^ 2 * h ^ 2 / ( 8 * m 2 * L 2 ^ 2 ) ; // t h i r d e ne rg y s t a t e o f g r a i n o f d u st

28 disp ( E g 3 , t hi r d e n e r g y s t a t e o f g r a in o f d u s t i s );29 K E = m 2 * v 1 ^ 2 / 2 ; // k i n e t i c e ne rg y o f g r a in o f d us t ;30 disp ( K E , k i n e t i c e n er g y o f g r a i n o f d u s t i s ) ;31 disp ( The e n e r g y l e v e l s o f a g r a i n o f d u s t a re s o

n ea r t o e a c h o t h er t ha t t h ey c o n s t i t u t e aco nt in uum . These e ne rg y l e v e l s a r e f a r s m a l l e rt han t he k i n e t i c e ne rg y p o ss e ss e d b y t h e g r ai n o f

d us t . I t can move t hr ou gh a l l t h es e e ne rg y l e v e l sw i th o ut an e x t e r n a l s u p pl y o f e n er g y . Thus

q u a n t i z a t i o n o f e n e r g y l e v e l s i s n o t a t a l l

s i g n i f i c a n t i n c as e o f m ac ro sc op ic b o d i e s . )

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Chapter 14

Lasers

Scilab code Exa 14.1 calculation of intensity of laser beam

1 clc ; clear ;

2 / / E x am pl e 1 4 . 13 / / c a l c u l a t i o n o f i n t e n s i t y o f l a s e r beam4

5 / / g i v e n v a l u e s6 P = 1 0 * 1 0 ^ - 3 ; / / P ow er i n Watt7 d = 1 . 3 * 1 0 ^ - 3 ; / / d i a m e t r e i n m8 A = % p i * d ^ 2 / 4 ; / / a r e a i n m 29

10

11 // c a l c u l a t i o n12 I = P / A ;

13 disp (I , i n t e n s i t y ( i n W/m 2 ) i s ) ;

Scilab code Exa 14.2 calculation of intensity of laser beam

1 clc ; clear ;

2 / / E x am pl e 1 4 . 2

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3 / / c a l c u l a t i o n o f i n t e n s i t y o f l a s e r beam

45 / / g i v e n v a l u e s6 P = 1 * 1 0 ^ - 3 ; / / P ow er i n Watt7 l = 6 3 2 8 * 1 0 ^ - 1 0 ; / / w a v el e n g th i n m8 A = l ^ 2 ; / / a r e a i n m 29

10

11 // c a l c u l a t i o n12 I = P / A ;

13 disp (I , i n t e n s i t y ( i n W/m 2 ) i s ) ;

Scilab code Exa 14.3 calculation of coherence length bandwidth and linewidth

1 clc ; clear ;

2 / / E x am pl e 1 4 . 33 // c a l c u l a t i o n o f c o h er e nc e l en g th , ba nd wid th and l i n e

w i dt h4

5 / / g i v e n v a l u e s6 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s7 t = . 1 * 1 0 ^ - 9 ; // t i m e d i v i s i o n i n s8 l = 6 2 3 8 * 1 0 ^ - 1 0 ; / / w a v el e n g th i n m9

10 // c a l c u l a t i o n11 x = c * t ;

12 disp (x , c o h er e n ce l e n g th ( i n m) i s ) ;13 d = 1 / t ;

14 disp (d , b an dw id th ( i n Hz ) i s ) ;

15 y = l ^ 2 * d / c ; // l i n e wi dt h i n m16 disp ( y * 1 0 ^ 1 0 , l i n e w id th ( i n a r ms tr o ng ) i s ) ;

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Scilab code Exa 14.4 calculation of frequency difference

1 clc ; clear ;

2 / / E x am pl e 1 4 . 43 // c a l c u l a t i o n o f f re q u e n c y d i f f e r e n c e4

5 / / g i v e n v a l u e s6 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s7 l = . 5 ; // d i s t a n c e i n m8

9 // c a l c u l a t i o n10 f = c / ( 2 * l ) ; / / i n h e r t z

11 disp ( f / 1 0 ^ 6 , f r e qu e n cy d i f f e r e n c e ( i n MHz) i s ) ;

Scilab code Exa 14.5 calculation of frequency difference

1 clc ; clear ;

2 / / E x am pl e 1 4 . 53 / / c a l c u l a t i o n o f no o f c a v i t y modes4

5 / / g i v e n v a l u e s6 c = 3 * 1 0 ^ 8 ; // v e l o c i t y o f l i g h t i n m/ s7 n = 1 . 7 5 ; // r e f r a c t i v e i nd ex8 l = 2 * 1 0 ^ - 2 ; // l e ng t h o f ruby r o d i n m9 x = 6 9 4 3 * 1 0 ^ - 1 0 ; / / w a v el e n g th i n m

10 y = 5 . 3 * 1 0 ^ - 1 0 ; // s p re ad o f w av el en gt h i n m11

12 // c a l c u l a t i o n13 d = c / n / l ;

14 f = c * y / x ^ 2 ;

15 m = f / d ;16 disp (m , no o f modes i s ) ;

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Chapter 15

Atomic nucleus and nuclear

energy

Scilab code Exa 15.1 calculation of binding energy per nucleon

1 clc ; clear ;

2 / / E x am pl e 1 5 . 13 // c a l c u l a t i o n o f b i nd i ng e ne rg y p er n uc le on4

5 / / g i v e n v a l u e s6 M p = 1 . 0 0 8 1 4 ; / / mass o f p r ot o n i n amu7 M n = 1 . 0 0 8 6 6 5 ; // m ass o f n u c le o n i n amu8 M = 7 . 0 1 8 2 2 ; / / mass o f L it hi um n u c l e u s i n amu9 a m u = 9 3 1 ; //amu i n MeV

10 n = 7 - 3 ; // no o f n e u tr on s i n l i t hi u m n u cl e u s11

12 // c a l c u l a t i o n13 E T = ( 3 * M p + 4 * M n - M ) * a m u ; / / t o t a l b i n d i n g e n er g y i n MeV14 E = E T / 7 ; / / 7 1 s t h e ma ss number

15 disp (E , B i nd i ng e n er g y p er n u c le o n i n MeV i s ) ;

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Scilab code Exa 15.2 calculation of energy

1 clc ; clear ;

2 / / E x am pl e 1 5 . 23 // c a l c u l a t i o n o f e ne rg y4

5 / / g i v e n v a l u e s6 M 1 = 1 5 . 0 0 0 0 1 ; / / a t o m ic m as s o f N15 i n amu7 M 2 = 1 5 . 0 0 3 0 ; / / a t o m ic m as s o f O15 i n amu8 M 3 = 1 5 . 9 9 4 9 ; / / a t o m ic m as s o f O16 i n amu9 a m u = 9 3 1 . 4 ; //amu in MeV

10 m p = 1 . 0 0 7 2 7 6 6 ; / / r e s t m a s s o f p r ot o n

11 m n = 1 . 0 0 8 6 6 5 4 ; / / r e s t m a s s o f n e ut r on12

13 // c a l c u l a t i o n14 Q 1 = ( M 3 - m p - M 1 ) * a m u ;

15 disp ( Q 1 , e n er g y r e q u i r e d t o rem ov e o ne p r ot o n fr omO16 i s ) ;

16 Q 2 = ( M 3 - m n - M 2 ) * a m u ;

17 disp ( Q 2 , e n er g y r e q u i r e d t o rem ov e o ne n e ut r on f ro mO16 i s ) ;

Scilab code Exa 15.3 calculation of binding energy

1 clc ; clear ;

2 / / E x am pl e 1 5 . 33 // c a l c u l a t i o n o f b i nd i ng e ne rg y4

5 / / g i v e n v a l u e s6 M p = 1 . 0 0 7 5 8 ; / / mass o f p r ot o n i n amu

7 M n = 1 . 0 0 8 9 7 ; / / mass o f n u c le o n i n amu8 M = 4 . 0 0 2 8 ; // m ass o f H el iu m n u c l e u s i n amu9 a m u = 9 3 1 . 4 ; //amu in MeV

10


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12 E 1 = ( 2 * M p + 2 * M n - M ) * a m u ; // t o t a l b i n di n g e ne rg y

13 disp ( E 1 , B i n di n g e n e r g y i n MeV i s ) ;14 E 2 = E 1 * 1 0 ^ 6 * 1 . 6 * 1 0 ^ - 1 9 ;15 disp ( E 2 , b i nd i n g e ne rg y i n J ou l e i s ) ;

Scilab code Exa 15.4 calculation of binding energy

1 clc ; clear ;

2 / / E x am pl e 1 5 . 4

3 // c a l c u l a t i o n o f amount o f u nch ang ed m a t e r i a l45 / / g i v e n v a l u e s6 T = 2 ; // h a l f l i f e i n y e a rs7 k = . 6 9 3 1 / T ; / / d ec ay c o n s t a n t8 M = 4 . 0 0 2 8 ; // m ass o f H el iu m n u c l e u s i n amu9 a m u = 9 3 1 . 4 ; //amu in MeV

10 N o = 1 ; // i n i t i a l amount in g11

12 // c a l c u l a t i o n13 N = N o * ( % e ^ ( - k * 2 * T ) ) ;

14 disp (N , a mount o f m a t e r i a l r e ma i n i ng u nc ha ng ed a f t e rf o u r y e a r s ( i n gram ) i s ) ;

Scilab code Exa 15.5 calculation of halflife

1 clc ; clear ;

2 / / E x am pl e 1 5 . 53 / / c a l c u l a t i o n o f amount o f h a l f l i f e

45 / / g i v e n v a l u e s6 t = 5 ; // t im e p e ri o d i n y e a r s7 a m u = 9 3 1 . 4 ; //amu in MeV8 N o = 5 ; // i n i t i a l amount in g

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9 N = 5 - ( 1 0 . 5 * 1 0 ^ - 3 ) ; // amount p r e s e n t a f t e r 5 y e a rs

1011

12 // c a l c u l a t i o n13 k = log ( N / N o ) / t ; // d e ca y c o n s t a n t14 T = - . 6 9 3 / k ;

15 disp (T , h a l f l i f e i n y e a r s i s ) ;

Scilab code Exa 15.6 calculation of activity

1 clc ; clear ;

2 / / E x am pl e 1 5 . 63 / / c a l c u l a t i o n o f a c t i v i t y4

5 / / g i v e n v a l u e s6 t = 2 8 ; // h a l f l i f e i n y e a r s7 m = 1 0 ^ - 3 ; / / ma ss o f s a mp l e8 M = 9 0 ; / / a to m ic mass o f s t r o n ti u m9 N A = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r

10

1112 // c a l c u l a t i o n13 n = m * N A / M ; // no o f n u c l e i i n 1 mg s am pl e14 k = . 6 9 3 / ( t * 3 6 5 * 2 4 * 6 0 * 6 0 ) ; // d e ca y c o n s t a n t15 A = k * n ;

16 disp (A , a c t i v i t y o f s am pl e ( i n d i s i n t e g r a t i o n s p ers e co n d ) i s ) ;

Scilab code Exa 15.7 calculation of age of mineral

1 clc ; clear ;

2 / / E x am pl e 1 5 . 73 // c a l c u l a t i o n o f a ge o f m i n er al

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4

5 / / g i v e n v a l u e s6 t = 4 . 5 * 1 0 ^ 9 ; // h a l f l i f e i n y e a rs7 M 1 = 2 3 8 ; // a t o mi c mass o f Uranium i n g8 m = . 0 9 3 ; // mass o f l e a d i n 1 g o f uranium i n g9 N A = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r

10 M 2 = 2 0 6 ; // a t o mi c m ass o f l e ad i n g11

12 // c a l c u l a t i o n13 n = N A / M 1 ; // no o f n u c l e i i n 1 g o f uranium sa mp le14 n 1 = m * N A / M 2 ; // no o f n u c l e i i n m mass o f l e a d15 c = n 1 / n ;

16 k = . 6 9 3 / t ; // d e ca y c o n s t a n t17 T = ( 1 / k ) * log ( 1 + c ) ;

18 disp (T , a g e o f m in er al i n y ea r s i s ) ;

Scilab code Exa 15.8 calculation of age of wooden piece

1 clc ; clear ;

2 / / E x am pl e 1 5 . 83 // c a l c u l a t i o n o f a ge o f wooden p i e c e4

5 / / g i v e n v a l u e s6 t = 5 7 3 0 ; // h a l f l i f e o f C14 i n y e a rs7 M 1 = 5 0 ; // mass o f wooden p i e c e i n g8 A 1 = 3 2 0 ; // a c t i v i t y o f wooden p i e c e ( d i s i n t e g r a t i o n

p er m in ut e p er g )9 A 2 = 1 2 ; // a c t i v i t y o f l i v i n g t r e e

10


12 k = . 6 9 3 / t ; // d e ca y c o n s t a n t13 A = A 1 / M 1 ; // a c t i v i t y a f t e r d ea th14

15 T = ( 1 / k ) * log ( A 2 / A ) ;

16 disp (T , a g e o f m in er al i n y ea r s i s ) ;

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Scilab code Exa 15.9 calculation of energy released

1 clc ; clear ;

2 / / E x am pl e 1 5 . 93 // c a l c u l a t i o n o f e n er gy r e l e a s e d4

5 / / g i v e n v a l u e s6 M 1 = 1 0 . 0 1 6 1 2 5 ; / / a to m ic mass o f Boron i n amu

7 M 2 = 1 3 . 0 0 7 4 4 0 ; / / a to m ic mass o f C13 i n amu8 M 3 = 4 . 0 0 3 8 7 4 ; / / a t o m ic m as s o f H el iu m i n amu9 m p = 1 . 0 0 8 1 4 6 ; // m ass o f p r ot o n i n amu

10 a m u = 9 3 1 ; //amu i n MeV11

12 // c a l c u l a t i o n13 Q = ( M 1 + M 3 - ( M 2 + m p ) ) * a m u ; // t o t a l b i n di n g e ne rg y i n M14 disp (Q , B i nd i ng e n er g y p er n u c le o n i n MeV i s ) ;

Scilab code Exa 15.10 calculation of crossection

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 03 / / c a l c u l a t i o n o f c r o s s s e c t i o n4

5 / / g i v e n v a l u e s6 t = . 0 1 * 1 0 ^ - 3 ; // t h i c k n e s s i n m7 n = 1 0 ^ 1 3 ; // no o f p r ot o ns bo mb ard ing t a r g e t p er s

8 N A = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r9 M = 7 ; // a t o mi c mass o f l i t hi u m i n kg10 d = 5 0 0 ; // d e n s i t y o f l i t h i u m i n kg /m311 n 0 = 1 0 ^ 8 ; // no o f n e ut r on s p ro du ce d p er s12 // c a l c u l a t i o n

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13 n 1 = d * N A / M ; // no o f t a r g e t n u c l e i p er u n it volume

14 n 2 = n 1 * t ; // no o f t a r ge t n u c l e i p er a re a15 A = n 0 / ( n * n 2 ) ;16 disp (A , c r o s s s e c t i o n ( i n m 2) f o r t h i s r e a c t i o n i s ) ;

Scilab code Exa 15.11 calculation of final energy

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 1

3 / / c a l c u l a t i o n o f f i n a l e ne rg y45 / / g i v e n v a l u e s6 B = . 4 ; //max mag net ic f i e l d in Wb/m27 c = 3 * 1 0 ^ 8 ;

8 e = 1 . 6 * 1 0 ^ - 1 9 ;

9 d = 1 . 5 2 ; / / d i a m e t r e i n m10 r = d / 2 ;

11

12 // c a l c u l a t i o n13 E = B * e * r * c ; //E=pc , p=mv=Ber

14 disp (E , f i n a l e ne rg y o f e ( i n J ) i s ) ;15 E 1 = ( E / e ) / 1 0 ^ 6 ;

16 disp ( E 1 , f i n a l e ne rg y o f e ( i n MeV) i s ) ;

Scilab code Exa 15.12 calculation of amount of fuel

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 2

3 // c a l c u l a t i o n o f amount o f f u e l4

5 / / g i v e n v a l u e s6 P = 1 0 0 * 1 0 ^ 6 ; // p ower r e q u i r e d by c i t y7 M = 2 3 5 ; / / a to m ic mass o f Uranium i n g

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8 e = 2 0 / 1 0 0 ; // c o n ve r si o n e f f i c i e n c y

9 N A = 6 . 0 2 * 1 0 ^ 2 6 ; / / a v o g a d r o s n um be r10 E = 2 0 0 * 1 0 ^ 6 * 1 . 6 * 1 0 ^ - 1 9 ; / / e n e r g y r e l e a s e d p e r f i s s i o n11 t = 8 . 6 4 * 1 0 ^ 4 ; // day i n s e co n d s12

13

14 // c a l c u l a t i o n15 E 1 = P * t ; / / e n e r g y r e q u i r e m e n t16 m = E 1 * M / ( N A * e * E ) ; / / no o f n u c l e i N=NAm/M, e ne rg y

r e l e a s e d by m kg i s NE , e n e r g y r e q u i r e m e n t =eNE17 disp (m , amount o f f u e l ( i n kg ) r e q u i r e d i s ) ;

Scilab code Exa 15.13 calculation of power output

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 33 // c a l c u l a t i o n o f power o ut pu t4

5 / / g i v e n v a l u e s6 M = 2 3 5 ; / / a to m ic mass o f Uranium i n kg7 e = 5 / 1 0 0 ; // r e a c t o r e f f i c i e n c y8 m = 2 5 / 1 0 0 0 ; / / amount o f u ra ni um co ns um ed p e r d ay i n kg9 E = 2 0 0 * 1 0 ^ 6 * 1 . 6 * 1 0 ^ - 1 9 ; / / e n e r g y r e l e a s e d p e r f i s s i o n

10 t = 8 . 6 4 * 1 0 ^ 4 ; // day i n s e co n d s11 N A = 6 . 0 2 * 1 0 ^ 2 6 ; / / a v o g a d r o s n um be r12

13 // c a l c u l a t i o n14 n = N A * m / M ; // no o f n u c l e i i n 25 g15 E 1 = n * E ; // e n er g y p ro du ce d by n n u c l e i16 E 2 = E 1 * e ; / / e n e r g y c o n v e r t e d t o p ow er

17 P = E 2 / t ; / / p ow er o u tp u t i n Watt18 disp ( P / 1 0 ^ 6 , p ow er o u t p u t i n MW i s ) ;

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Scilab code Exa 15.14 calculation of power developed

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 43 // c a l c u l a t i o n o f power d ev e lo p ed4

5 / / g i v e n v a l u e s6 M = 2 3 5 ; / / a to m ic mass o f Uranium i n kg7 m = 2 0 . 4 ; / / amount o f u ra ni um co ns um ed p e r d ay i n kg8 E = 2 0 0 * 1 0 ^ 6 * 1 . 6 * 1 0 ^ - 1 9 ; / / e n e r g y r e l e a s e d p e r f i s s i o n9 t = 3 6 0 0 * 1 0 0 0 ; // t im e o f o p e ra t i on

10 N A = 6 . 0 2 * 1 0 ^ 2 6 ; / / a v o g a d r o s n um be r

1112 // c a l c u l a t i o n13 n = N A * m / M ; // no o f n u c l e i i n 2 0 . 4 kg14 E 1 = n * E ; // e n er g y p ro du ce d by n n u c l e i15 P = E 1 / t ; // in Watt16 disp ( P / 1 0 ^ 6 , p o we r d e v e l o p e d i n MW i s ) ;

Scilab code Exa 15.15 calculation of amount of dueterium consumed

1 clc ; clear ;

2 / / E x am pl e 1 5 . 1 53 / / c a l c u l a t i o n o f amount o f d u et er i um co nsu med4

5 / / g i v e n v a l u e s6 M 1 = 2 . 0 1 4 7 8 ; / / a t o m ic m as s o f H yd ro ge n i n amu7 M 2 = 4 . 0 0 3 8 8 ; / / a t o m ic m as s o f H el iu m i n amu8 a m u = 9 3 1 ; //amu i n MeV9 e = 3 0 / 1 0 0 ; // e f f i c i e n c y

10 P = 5 0 * 1 0 ^ 6 ; / / o u t p u t p ow er11 N A = 6 . 0 2 6 * 1 0 ^ 2 6 ; / / a v o g a d r o n um be r12 t = 8 . 6 4 * 1 0 ^ 4 ; // s e c o n ds i n a day13


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15 Q = ( 2 * M 1 - M 2 ) * a m u ; // e ne rg y r e l e a s e d i n a DD r e a c t i o n

i n MeV16 O = Q * e * 1 0 ^ 6 / 2 ; / / a c t u a l o ut p ut p e r d u et e ri u m atom i neV

17 n = P / ( O * 1 . 6 * 1 0 ^ - 1 9 ) ; // no o f D a toms r e q u i r e d18 m = n * M 1 / N A ; // e q u i v al e n t mass o f D r e q ui r e d p er s19 X = m * t ;

20

21 disp (X , D eu te ri um r e q u ir e m en t p e r day i n kg i s ) ;

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Chapter 16

Structure of Solids

Scilab code Exa 16.1 calculation of density

1 clc ; clear ;

2 / / E x am pl e 1 6 . 13 // c a l c u l a t i o n o f d e ns i t y4

5 / / g i v e n v a l u e s6 a = 3 . 3 6 * 1 0 ^ - 1 0 ; / / l a t t i c e c o n s t a n t i n m7 M = 2 0 9 ; / / a to mi cm as s o f p ol on iu m i n kg8 N = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r9 z = 1 ; / / no o f atom

10 // c a l c u l a t i o n11 d = z * M / ( N * a ^ 3 )

12

13 disp (d , d e n s i t y ( i n kg /m 3 ) i s ) ;

Scilab code Exa 16.2 calculation of no of atoms

1 clc ; clear ;

2 / / E x am pl e 1 6 . 2

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3 // c a l c u l a t i o n o f no o f atoms

45 / / g i v e n v a l u e s6 a = 4 . 3 * 1 0 ^ - 1 0 ; // e dg e o f u n it c e l l i n m7 d = 9 6 3 ; / / d e n s i t y i n kg /m 38 M = 2 3 ; / / a to mi cm as s o f s od iu m i n kg9 N = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r

10

11 // c a l c u l a t i o n12 z = d * N * a ^ 3 / M ;

13

14 disp (z , no o f atoms i s ) ;

Scilab code Exa 16.3 calculation of distance

1 clc ; clear ;

2 / / E x am pl e 1 6 . 33 // c a l c u l a t i o n o f d i s t a n c e4

5 / / g i v e n v a l u e s6 z = 4 ; // no o f atoms i n f c c7 d = 2 1 8 0 ; / / d e n s i t y i n k g /m 38 M = 2 3 + 3 5 . 3 ; // a to mi cm as s o f so dium c h l o r i d e i n kg9 N = 6 . 0 2 * 1 0 ^ 2 6 ; // av ogadr o s numbe r

10

11 // c a l c u l a t i o n12 a 1 = z * M / ( N * d ) ;

13 a = a 1 ^ ( 1 / 3 ) ;

14 l = a / 2 ; / / i n m15

16 disp ( l * 1 0 ^ 1 0 , d i s t a n c e b et we en a d j a ce n t c h l o r i n e ands od iu m a to ms i n a r ms t ro n g i s ) ;

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Scilab code Exa 16.4 calculation of interatomic spacing

1 clc ; clear ;

2 / / E x am pl e 1 6 . 43 / / c a l c u l a t i o n o f i n t e ra t o m i c s p ac i ng4

5 / / g i v e n v a l u e s6 a l p h a = 3 0 * % p i / 1 8 0 ; // B ragg a n g l e i n d e g re e7 h = 1 ;

8 k = 1 ;

9 l = 1 ;

10 m = 1 ; // o r d e r o f r e f l e c t i o n

11 x = 1 . 7 5 * 1 0 ^ - 1 0 ; / / w a v el e n g th i n m12

13 // c a l c u l a t i o n14 d = m * x / ( 2 * sin ( a l p h a ) ) ;

15 a = d * sqrt ( h ^ 2 + k ^ 2 + l ^ 2 ) ; / / i n m16

17 disp ( a * 1 0 ^ 1 0 , i n t e r a t o m i c s p a ci n g i n a rm st ro ng i s ) ;

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Chapter 17

The Band Theory of Solids

Scilab code Exa 17.1 calculation of velocity of fraction of free electrone

1 clc ; clear ;

2 / / E x am pl e 1 7 . 13 // c a l c u l a t i o n o f p r o b a b i l i t y4

5 / / g i v e n v a l u e s6 E = . 0 1 ; // e ne rg y d i f f e r e n c e i n eV7 k T = . 0 2 6 ; / / t e mp e r tu r e e q u i v a l e n t a t room temp i n e8

9 // c a l c u l a t i o n10 P = 1 / ( 1 + ( % e ^ ( E / k T ) ) ) ;

11

12 disp (P , i n t e r a t o m i c s p a c i ng i s ) ;

Scilab code Exa 17.2 calculation of velocity of e

1 clc ; clear ;

2 / / E x am pl e 1 7 . 23 / / c a l c u l a t i o n o f v e l o c i t y o f e

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4

5 / / g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ; // c ha rg e o f e i n C7 E = 2 . 1 * e ; // f er mi l e v e l i n J8 m = 9 . 1 * 1 0 ^ - 3 1 ; // mass o f e i n kg9

10 // c a l c u l a t i o n11 v = sqrt ( 2 * E / m ) ;

12

13 disp (v , v e l o c i t y o f e ( i n m/ s ) ) ;

Scilab code Exa 17.3 calculation of velocity of fraction of free electrones

1 clc ; clear ;

2 / / E x am pl e 1 7 . 33 / / c a l c u l a t i o n o f v e l o c i t y o f f r a c t i o n o f f r e e

e l e c t r o n s4

5 / / g i v e n v a l u e s6 E = 5 . 5 ; // f e r m i l e v e l i n eV7 k T = . 0 2 6 ; / / t e mp e r tu r e e q u i v a l e n t a t room temp i n e8

9 // c a l c u l a t i o n10 f = 2 * k T / E ;

11

12 disp (f , f r a c t i o n o f f r e e e l e c t r o n e\ s u pt o w id th kTon e i t h e r s i d e o f Ef i s ) ;

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Chapter 18

Semiconductors

Scilab code Exa 18.2 calculation of probability

1 clc ; clear ;

2 / / E x am pl e 1 8 . 23 // c a l c u l a t i o n o f p r o b a b i l i t y4

5 / / g i v e n v a l u e s6 T = 3 0 0 ; / / temp i n K7 k T = . 0 2 6 ; / / t e mp e r tu r e e q u i v a l e n t a t room temp i n eV8 E g = 5 . 6 ; // f o r b i d d e n g ap i n eV9

10 // c a l c u l a t i o n11 f = 1 / ( 1 + % e ^ ( E g / ( 2 * k T ) ) ) ;

12

13 disp (f , p r o b a b i l i t y o f an e b ei n g t h e rm a l l y prom otedt o c o nd u ct i on band i s ) ;

Scilab code Exa 18.3 calculation of fraction of e in CB

1 clc ; clear ;

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2 / / E x am pl e 1 8 . 3

3 // c a l c u l a t i o n o f f r a c t i o n o f e i n CB45 / / g i v e n v a l u e s6 T = 3 0 0 ; / / temp i n K7 k T = . 0 2 6 ; / / t e mp e r tu r e e q u i v a l e n t a t room temp i n eV8 E g 1 = . 7 2 ; / / f o r b i d d e n g ap o f g erm an ium i n eV9 E g 2 = 1 . 1 ; // f o r b i dd e n gap o f s i l i c o n i n eV

10 E g 3 = 5 . 6 ; / / f o r b i d d e n ga p o f diamond i n eV11

12 // c a l c u l a t i o n13 f 1 = % e ^ ( - E g 1 / ( 2 * k T ) ) ;

14 disp ( f 1 , f r a c t i o n o f e i n c on du c ti on band o f g er ma ni um i s ) ;

15 f 2 = % e ^ ( - E g 2 / ( 2 * k T ) ) ;

16 disp ( f 2 , f r a c t i o n o f e i n c on du c ti on band o f s i l i c o n i s ) ;

17 f 3 = % e ^ ( - E g 3 / ( 2 * k T ) ) ;

18 disp ( f 3 , f r a c t i o n o f e i n c on du c ti on band o f diamond i s ) ;

Scilab code Exa 18.4 calculation of fractionional change in no of e

1 clc ; clear ;

2 / / E x am pl e 1 8 . 33 // c a l c u l a t i o n o f f r a c t i o n i o n a l c ha n ge i n no o f e4

5 / / g i v e n v a l u e s6 T 1 = 3 0 0 ; / / temp i n K7 T 2 = 3 1 0 ; / / temp i n K

8 E g = 1 . 1 ; // f o r b i d de n gap o f s i l i c o n i n eV9 k = 8 . 6 * 1 0 ^ - 5 ; / / b o lt zm a nn s c o n s t a n t i n eV /K

10

11 // c a l c u l a t i o n12 n 1 = ( 1 0 ^ 2 1 . 7 ) * ( T 1 ^ ( 3 / 2 ) ) * 1 0 ^ ( - 2 5 0 0 * E g / T 1 ) ; // no o f

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c o nd u ct i on e a t T1

13 n 2 = ( 1 0 ^ 2 1 . 7 ) * ( T 2 ^ ( 3 / 2 ) ) * 1 0 ^ ( - 2 5 0 0 * E g / T 2 ) ; // no o f c o nd u ct i on e a t T214 x = n 2 / n 1 ;

15 disp (x , f r a c t i o n a l c ha n g e i n no o f e i s ) ;

Scilab code Exa 18.5 calculation of resistivity

1 clc ; clear ;

2 / / E x am pl e 1 8 . 53 / / c a l c u l a t i o n o f r e s i s t i v i t y4

5 / / g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ;

7 n i = 2 . 5 * 1 0 ^ 1 9 ; / / i n t r i n s i c d e n s i t y o f c a r r i e r s p e r m 38 u e = . 3 9 ; // m o b i l i t y o f e9 u h = . 1 9 ; // m o b i l i t y o f h o l e

10

11


13 c = e * n i * ( u e + u h ) ; / / c o n d u c t i v i t y14 r = 1 / c ; // r e s i s t i v i t y15 disp (r , r e s i s t i v i t y in ohm m i s ) ;

Scilab code Exa 18.6 calculation of conductivity of intrinsic and dopedsemiconductors

1 clc ; clear ;

2 / / E x am pl e 1 8 . 63 / / c a l c u l a t i o n o f c o n d u c t i v i t y o f i n t r i n s i c and d op ed

s e m i c o n d u c t o r s4


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6 h = 4 . 5 2 * 1 0 ^ 2 4 ; // no o f h o l e s p er m3

7 e = 1 . 2 5 * 1 0 ^ 1 4 ; // no o f e l e c t r o n s p er m38 u e = . 3 8 ; // e m o b i l i t y9 u h = . 1 8 ; // h o l e m o b i l i t y

10 q = 1 . 6 * 1 0 ^ - 1 9 ; // c ha rg e o f e i n C11 // c a l c u l a t i o n12 ni = sqrt ( h * e ) ; // i n t r i n s i c c o nc e n t r at i o n13 c i = q * n i * ( u e + u h ) ;

14 disp ( c i , c o n d u c t i v i t y o f s e m i co n d u ct o r ( i n S /m) i s ) ;15 c p = q * h * u h ;

16 disp ( c p , c o n d u c t i v i t y o f d op ed s e m ic o n d uc t o r ( i n S /m) i s ) ;

Scilab code Exa 18.7 calculation of hole concentration

1 clc ; clear ;

2 / / E x am pl e 1 8 . 73 / / c a l c u l a t i o n o f h o l e c o n c e n t r a t i o n4


6 n i = 2 . 4 * 1 0 ^ 1 9 ; // c a r r i e r c o n c e n t r a t i o n p er m37 N = 4 * 1 0 ^ 2 8 ; / / c o n c e n t r a t i o n o f g e a to ms p e r m 38

9 // c a l c u l a t i o n10 N D = N / 1 0 ^ 6 ; / / d on or c o c n t r t n11 n = N D ; // no o f e l e c t r o n e s12

13 p = n i ^ 2 / n ;

14 disp (p , c o n c e n t ar t i o n o f h o l e s p er m3 i s ) ;

Scilab code Exa 18.8 calculation of Hall voltage

1 clc ; clear ;

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2 / / E x am pl e 1 8 . 8

3 // c a l c u l a t i o n o f H al l v o l t a ge45 / / g i v e n v a l u e s6 N D = 1 0 ^ 2 1 ; // d o no r d e n s i t y p e r m 37 B = . 5 ; / / m a g n et i c f i e l d i n T8 J = 5 0 0 ; / / c u r r e n t d e n s i t y i n A/m 29 w = 3 * 1 0 ^ - 3 ; // w id th i n m

10 e = 1 . 6 * 1 0 ^ - 1 9 ; / / c h a rg e i n C11

12 // c a l c u l a t i o n13

1415 V = B * J * w / ( N D * e ) ; // i n v o l t s16 disp ( V * 1 0 ^ 3 , H a ll v o l t ag e i n mv i s ) ;

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Chapter 19

PN Junction Diode

Scilab code Exa 19.1 calculation of potential barrier

1 clc ; clear ;

2 / / E x am pl e 1 9 . 13 // c a l c u l a t i o n o f p o t e n t i a l b a r r i e r4

5 / / g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ;

7 n = 4 . 4 * 1 0 ^ 2 8 ; // no o f a to ms p e r m 38 k T = . 0 2 6 * e ; / / temp e q v l n t a t room temp9 n i = 2 . 4 * 1 0 ^ 1 9 ; / / no o f i n t r i n s i c c a r r i e r s p e r m 3

10 N A = n / 1 0 ^ 6 ; // no o f a c c e p t o r s11 N D = n / 1 0 ^ 6 ; // no o f d on or s12

13 // c a l c u l a t i o n14 V = ( k T / e ) * log ( N A * N D / n i ^ 2 ) ;

15 disp (V , p o t e n t i a l b a r r i e r i n v o l t s i s ) ;

Scilab code Exa 19.2 calculation of current

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1 clc ; clear ;

2 / / E x am pl e 1 9 . 23 / / c a l c u l a t i o n o f c u r r e nt4

5 / / g i v e n v a l u e s6 e = 1 . 6 * 1 0 ^ - 1 9 ;

7 k T = . 0 2 6 * e ; / / temp e q v l n t a t room temp8 I o = 2 * 1 0 ^ - 7 ; // c u r r e n t f l o w i n g a t room temp i n A9 V = . 1 ; // f or wa rd b i a s v o l t a g e i n v o l t s

10

11 // c a l c u l a t i o n12 I = I o * ( % e ^ ( e * V / k T ) - 1 ) ; // in Ampere

13 disp ( I * 1 0 ^ 6 , c u r r e nt f l o w i n g when f o rw ar d b i a sa p p l i e d ( i n m i c ro a m pe r e ) i s ) ;

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Chapter 21

Magnetic Materials

Scilab code Exa 21.1 calculation of magnetizing force and relative perme-ability

1 clc ; clear ;

2 / / E x am pl e 2 1 . 13 // c a l c u l a t i o n o f m ag ne ti zi ng f o r c e and r e l a t i v e

p e r m e a b i l i t y4

5 / / g i v e n v a l u e s6 M = 2 3 0 0 ; / / m a g n e t i z a t i o n i n A/m7 B = . 0 0 3 1 4 ; / / f l u x d e n s i t y i n Wb/m 28 u = 1 2 . 5 7 * 1 0 ^ - 7 ; / / p e r m e a b i l i t y i n H/m9

10 // c a l c u l a t i o n11 H = ( B / u ) - M ;

12 disp (H , m a g n e t i z i n g f o r c e ( i n A/m) i s ) ;13 U r = B / ( u * H ) ;

14 disp ( U r , r e l a t i v e p e rm e ab i l i t y i s )

Scilab code Exa 21.2 calculation of magnetization and magnetic flux den-sity

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1 clc ; clear ;

2 / / E x am pl e 2 1 . 23 / / c a l c u l a t i o n o f m a g ne t iz a t io n and m ag ne ti c f l u xd e n s i t y

4

5 / / g i v e n v a l u e s6 H = 1 0 ^ 5 ; / / e x t e r n a l f i e l d i n A/m7 X = 5 * 1 0 ^ - 5 ; // s u s c e p t i b i l i t y8 u = 1 2 . 5 7 * 1 0 ^ - 7 ; / / p e r m e a b i l i t y i n H/m9

10 // c a l c u l a t i o n11 M = X * H ;

12 disp (M , m a g n e t i z a t i o n ( i n A/m) i s ) ;13 B = u * ( M + H ) ;

14 disp (B , m a gn et i c f l u x d e n s i t y ( i n wb/m 2 ) i s )

Scilab code Exa 21.3 calculation of relative permeability

1 clc ; clear ;

2 / / E x am pl e 2 1 . 33 / / c a l c u l a t i o n o f r e l a t i v e p e rm e ab i l i t y4

5 / / g i v e n v a l u e s6

7 X = 3 . 7 * 1 0 ^ - 3 ; // s u s c e p t i b i l i t y a t 300 k8 T = 3 0 0 ; / / temp i n K9 T 1 = 2 0 0 ; / / temp i n K

10 T 2 = 5 0 0 ; / / temp i n K11


13 C = X * T ; / / c u r i e c o n s t a n t14 X T 1 = C / T 1 ;

15 disp ( X T 1 , r e l a t i v e p e r m e a b i l i t y a t T1 i s ) ;16 X T 2 = C / T 2 ;

17 disp ( X T 2 , r e l a t i v e p e r m e ab i l i t y a t T2 i s )

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Chapter 22

Superconductivity

Scilab code Exa 22.1 calculation of magnetic field

1 clc ; clear ;

2 / / E x am pl e 2 2 . 13 / / c a l c u l a t i o n o f m a gn et i c f i e l d4

5 / / g i v e n v a l u e s6

7 T c = 7 . 2 ; // t r a n s i t i o n temp i n K8 T = 5 ; / / temp i n K9 H c = 3 . 3 * 1 0 ^ 4 ; / / m a g n e t i c f i e l d a t T i n A/m

10

11

12 // c a l c u l a t i o n13 H c 0 = H c / ( 1 - ( T ^ 2 / T c ^ 2 ) ) ;

14 disp ( H c 0 , max v a lu e o f H a t 0K ( i n A/m) i s ) ;

Scilab code Exa 22.2 calculation of transition temperature

1 clc ; clear ;

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2 / / E x am pl e 2 2 . 2

3 / / c a l c u l a t i o n o f t r a n s i t i o n t em pe ra tu re45 / / g i v e n v a l u e s6

7 T = 8 ; / / temp i n K8 H c = 1 * 1 0 ^ 5 ; // c r i t i c a l magn e t i c f i e l d at T i n A/m9 H c 0 = 2 * 1 0 ^ 5 ; / / m a g n et i c f i e l d a t 0 K i n A/m

10

11 // c a l c u l a t i o n12 T c = T / ( sqrt ( 1 - H c / H c 0 ) ) ;

13 disp ( T c , t r a n s i t i o n temp i n K i s ) ;

Scilab code Exa 22.3 calculation of temp at which there is max criticalfield

1 clc ; clear ;

2 / / E x am pl e 2 2 . 33 // c a l c u l a t i o n o f temp a t whi ch t h e r e i s max

c r i t i c a l f i e l d4

5 / / g i v e n v a l u e s6

7 T c = 7 . 2 6 ; // c r i t i c a l temp in K8 H c = 8 * 1 0 ^ 5 ; //max c r i t i c a l magn e t i c f i e l d at T i n A/m9 H = 4 * 1 0 ^ 4 ; // s u b j e c t e d m a gn et i c f i e l d a t i n A/m

10

11 // c a l c u l a t i o n12 T = T c * ( sqrt ( 1 - H / H c ) ) ;

13 disp (T , max t emp f o r s u p e r c o n d u c t i v i t y i n K i s ) ;

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Chapter 23

Dielectrics

Scilab code Exa 23.1 calculation of relative permittivity

1 clc ; clear ;

2 / / E x am pl e 2 3 . 13 // c a l c u l a t i o n o f r e l a t i v e p e r m i t t i v i t y4

5 / / g i v e n v a l u e s6

7 E = 1 0 0 0 ; // e l e c t r i c f i e l d i n V/m8 P = 4 . 3 * 1 0 ^ - 8 ; // p o l a r i z a t i o n i n C/m 29 e = 8 . 8 5 * 1 0 ^ - 1 2 ; // p e r m i t t i v i t y i n F/m

10

11

12 // c a l c u l a t i o n13 e r = 1 + ( P / ( e * E ) ) ;

14 disp ( e r , r e l a t i v e p e r m i t t i v i t y o f NaCl i s ) ;

Scilab code Exa 23.2 calculation of electronic polarizability

1 clc ; clear ;

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2 / / E x am pl e 2 3 . 2

3 / / c a l c u l a t i o n o f e l e c t r o n i c p o l a r i z a b i l i t y45 / / g i v e n v a l u e s6

7 e = 8 . 8 5 * 1 0 ^ - 1 2 ; // p e r m i t t i v i t y i n F/m8 e r = 1 . 0 0 2 4 ; // r e l a t i v e p e r m i t t i v i t y a t NTP9 N = 2 . 7 * 1 0 ^ 2 5 ; / / a to ms p e r m 3

10

11

12 // c a l c u l a t i o n13 a l p h a = e * ( e r - 1 ) / N ;

14 disp ( a l p h a , e l e c t r o n i c p o l a r i z a b i l i t y ( i n F/m 2) i s ) ;

Scilab code Exa 23.3 calculation of electronic polarizability and relativepermittivity

1 clc ; clear ;

2 / / E x am pl e 2 3 . 33 / / c a l c u l a t i o n o f e l e c t r o n i c p o l a r i z a b i l i t y and

r e l a t i v e p e r m i t t i v i t y4

5 / / g i v e n v a l u e s6

7 e = 8 . 8 5 * 1 0 ^ - 1 2 ; // p e r m i t t i v i t y i n F/m8 N = 9 . 8 * 1 0 ^ 2 6 ; / / a to ms p e r m 39 r = . 5 3 * 1 0 ^ - 1 0 ; // r a d i u s i n m

10

11

12 // c a l c u l a t i o n13 a l p h a = 4 * % p i * e * r ^ 3 ;

14 disp ( a l p h a , e l e c t r o n i c p o l a r i z a b i l i t y ( i n F/m 2) i s ) ;

15 e r = 1 + ( 4 * % p i * N * r ^ 3 ) ;

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16 disp ( e r , r e l a t i v e p e r m i t t i v i t y i s )

Scilab code Exa 23.4 calculation of electronic polarizability and relativepermittivity

1 clc ; clear ;

2 / / E x am pl e 2 3 . 43 / / c a l c u l a t i o n o f e l e c t r o n i c p o l a r i z a b i l i t y and

r e l a t i v e p e r m i t t i v i t y

45 / / g i v e n v a l u e s6 w = 3 2 ; // a t om ic w ei gh t o f s u l ph u r7 d = 2 . 0 8 * 1 0 ^ 3 ; / / d e n s i t y i n k g /m 38 N A = 6 . 0 2 * 1 0 ^ 2 6 ; / / a v o g a d r o s n um be r9 a l p h a = 3 . 2 8 * 1 0 ^ - 4 0 ; // e l e c t r o n i c p o l a r i z a b i l i t y i n F .m

210 e = 8 . 8 5 4 * 1 0 ^ - 1 2 ; / / p e r m i t t i v i y11 // c a l c u l a t i o n12

13 n = N A * d / w ;

14 k = n * a l p h a / ( 3 * e ) ;15 e r = ( 1 + 2 * k ) / ( 1 - k ) ;

16 disp ( e r , r e l a t i v e p e r m i t t i v i t y i s )

Scilab code Exa 23.5 calculation of ionic polarizability

1 clc ; clear ;

2 / / E x am pl e 2 3 . 5

3 / / c a l c u l a t i o n o f i o n i c p o l a r i z a b i l i t y4

5 / / g i v e n v a l u e s6 n = 1 . 5 ; // r e f r a c t i v e i nd ex7 e r = 6 . 7 5 ; // r e l a t i v e p e r m i t t i v i t y

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8

9 // c a l c u l a t i o n10 P i = ( e r - n ^ 2 ) * 1 0 0 / ( e r - 1 ) ;11 disp ( P i , p e r c e nt a g e i o n i c p o l a r i z a b i l i t y ( i n %) ) i s

)

Scilab code Exa 23.6 calculation of frequency and phase difference

1 clc ; clear ;

2 / / E x am pl e 2 3 . 63 / / c a l c u l a t i o n o f f r e q ue n cy and p ha se d i f f e r e n c e4

5 / / g i v e n v a l u e s6 t = 1 8 * 1 0 ^ - 6 ; // r e l a x a t i o n t i m e i n s7

8 // c a l c u l a t i o n9 f = 1 / ( 2 * % p i * t ) ;

10 disp (f , f r e qu e n cy a t wh ich r e a l and i m ag i na r y p a rto f c om pl x d i e l e c t r i c c o n s t a n t a r e e q u a l i s ) ;

11 a l p h a = atan ( 1 ) * 1 8 0 / % p i ; // p ha se d i f f e r e n c e bet w ee n

c u r r e nt and v o l t a g e ( 1 b e ca u se r e a l and i ma g in ryp a r t s a r e e q u a l o f t h e d i e l e c t r i c c o n s t a n t )

12 disp ( a l p h a , p ha se d i f f e e r e n c e ( i n d e g r e e ) i s ) ;

Scilab code Exa 23.7 calculation of frequency

1 clc ; clear ;

2 / / E x am pl e 2 3 . 7

3 // c a l c u l a t i o n o f f r e q ue n cy4

5 / / g i v e n v a l u e s6 t = 5 . 5 * 1 0 ^ - 3 ; // t h i c k n e s s o f p l a t e i n m7 Y = 8 * 1 0 ^ 1 0 ; //Young s modulus in N/m2

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8 d = 2 . 6 5 * 1 0 ^ 3 ; / / d e n s i t y i n k g /m 3

910

11

12 // c a l c u l a t i o n13 f = sqrt ( Y / d ) / ( 2 * t ) ; // i n Hz14 disp ( f / 1 0 ^ 3 , f r e q u e n c y o f f u n da m e nt a l n o t e ( i n KHz )

i s ) ;

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Chapter 24

Fibre optics

Scilab code Exa 24.1 Fiber optics numerical aperture calculation

1 clc ; clear ;

2 / / E x am pl e 2 4 . 13 / / F i b e r o p t i c s4

5 / / g i v e n v a l u e s6 n = 1 . 5 ; // r e f r a c t i v e i nd ex7 x = . 0 0 0 5 ; // f r a c t i o n a l i nd ex d i f f e r e n c e8

9 // c a l c u l a t i o n10 u = n * ( 1 - x ) ;

11 disp (u , c l a d d in g i nd ex i s ) ;12 a l p h a = asin ( u / n ) * 1 8 0 / % p i ;

13 disp ( a l p h a , c r i t i c a l i n t e r n a l r e f l e c t i o n a n g l e ( i nd e g r e e ) i s ) ;

14 t h e t a = asin ( sqrt ( n ^ 2 - u ^ 2 ) ) * 1 8 0 / % p i ;

15 disp ( t h e t a , c r i t i c a l a c c e p t a n c e a n g l e ( i n d e g r e e ) i s

) ;16 N = n * sqrt ( 2 * x ) ;

17 disp (N , n u me r ic a l a p e r tu r e i s ) ;

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Scilab code Exa 24.2 calculation of acceptance angle

1 clc ; clear ;

2 / / E x am pl e 2 4 . 23 // c a l c u l a t i o n o f a c c e p t a n ce a n gl e4

5 / / g i v e n v a l u e s6 n = 1 . 5 9 ; // c l ad d i ng r e f r a c t i v e i nd ex7 u = 1 . 3 3 ;

// r e f r a c t i v e i nd ex o f w at er8 N = . 2 0 ; // n u me r ic a l a p e r tu r e o f f i b r e9 // c a l c u l a t i o n

10 x = sqrt ( N ^ 2 + n ^ 2 ) ; // i nd ex o f f i b r e11 N1 = sqrt ( x ^ 2 - n ^ 2 ) / u ; // n u m e ri c a l a p e r t u r e when f i b r e

i s i n w a te r12 a l p h a = asin ( N 1 ) * 1 8 0 / % p i ;

13 disp ( a l p h a , a c c e p t a n ce a n gl e i n d e g r e e i s ) ;

Sc

A Textbook of Engineering Physics_M. N. Avadhanulu, And P. G. Kshirsagar

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Transcript of A Textbook of Engineering Physics_M. N. Avadhanulu, And P. G. Kshirsagar