bab 1 intorductions and planck theory

8/11/2019 Bab 1 Intorductions and Planck Theory

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QUANTUM PHYSICS

KFS 423

Dr. Abdurrahman, M.Si Antomi Saregar, S.Pd, M.Si


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2

0. Prelude -- Development of

Classical Physics and Dark Clouds

(before 20th century)


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3

Classical Mechanics

Newton, Sir Isaac, PRS,(1643 1727), Englishphysicist andmathematician

Euler, Leonhard(1707 -- 1783),Swissmathematician.

Lagrange, Joseph Louis(1736 -- 1813),Italian-French mathematician,astronomer and physicist.

Hamilton, William Rowan (1805 --1865),Irish mathematician andastronomer.


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4

Classical Electrodynamics

Coulomb, CharlesAugustin (1736 1806 ), French physicist

Biot, Jean Baptiste(1774 --1862), FrenchPhysicist;Savart, Flix (1791 --1841), French Physicist

Ampere, AndreMarie (1775 -- 1836),French Physicist

Faraday, Michael(1791 -- 1867),English Physicist

Lorentz, HendrikAntoon (1853 --1928), DutchPhysicist

Maxwell, James Clerk (1831 1879), Scottish physicist


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5

Classical Thermodynamics

Clausius, RudolfJulius Emanuel(1822 -- 1888) ,Germanmathematicalphysicist.

Thomson, William(Baron Kelvin) (1824 - 1907),

British physicistand mathematician.

Boltzmann, Ludwig, (1844

1906), Austrian physicist.

Helmholtz, Hermann

Ludwig Ferdinand von(1821 -- 1894), Germanphysicist and physician.

Carnot, Nicolas

Lonard Sadi (1796-- 1832),French physicist.

Dalton, John (1766

-- 1844), Britishchemist andphysicist.

Joule, James

Prescott (1818 --1889), Britishphysicist.

Maxwell, JamesClerk (1831 1879), Scottish

physicist
http://www.answers.com/main/ntquery?method=4&dsname=Wikipedia+Images&dekey=Johndalton.jpg


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6

Classical Statistical Mechanics

Boltzmann, Ludwig, (1844

1906), Austrian physicist.

Equal a priori probability postulate (Boltzmann)

Given an isolated system in equilibrium, it is found with equalprobability in each of its accessible microstates.

Microcanonical ensemble(independent system)

Canonical ensemble (isolated system)

Grandcanonical ensemble (opened system)


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7

Dark Clouds

Lord and Lady Kelvin at thecoronation of King EdwardVII in 1902.

Sir William Thomsonworking on a problem ofscience in 1890.

William Thomson produced 70patents in the U.K. from 1854to 1907.

There is nothing new to be discovered in physics now.

All that remains is more and more precise measurement.


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8

Dark Clouds

Nineteenth-Century Clou ds over the Dynam ical Theory of Heat and Light (27th April 1900, Lord Kelvin)

"Beauty and clearness of theory... Overshadowed by two clouds..."

Michelson, Albert Morley, Edward

Einstein, Albert Planck, MaxMichelson-Morley Experiment (1887)

Ultraviolet catastrophy in blackbody radiation (before October, 1900)


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Chapter 1 Thermal radiation and Plancks postulate

FUNDAMENTAL CONCEPTS OF QUANTUM

PHYSICS Thermal radiation: The radiation emitted by a body as a result of temperature.

Blackbody : A body that surface absorbs all the thermal radiation incident on

them.

Spectral radiancy : The spectral distribution of blackbody radiation .)(T R :)( d R T represents the emitted energy from a unit area per unit time

between and at absolute temperature T. d

1899 by Lummer andPringsheim


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The spectral radiancy of blackbody radiation shows that:

(1) little power radiation at very low frequency

(2) the power radiation increases rapidly as increases from very

small value.

(3) the power radiation is most intense at certain for particulartemperature.

(4) drops slowly, but continuously as increases

, and

(5) increases linearly with increasing temperature.

(6) the total radiation for all ( radiancy )

increases less rapidly than linearly with increasing temperature.

max

)(,max T R

.0)( T R

m ax

d R R T T )(0


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Stefans law (1879): 4284 /1067.5, K m W T R o T

Stefan-Boltzmann constant

Wiens displacement (1894): mK xT 3m ax 109.2.

1.3 Classical theory of cavity radiation

Rayleigh and Jeans (1900):

(1) standing wave with nodes at the metallic surface

(2) geometrical arguments count the number of standing waves

(3) average total energy depends only on the temperature

one-dimensional cavity:

one-dimensional electromagnetic standing wave

)2sin()2

sin(),( 0 t x

E t x E


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for all time t, nodes at .......3,2,1,0,/2 n n x

a nc n a n a a x

x

2//22

0

standing wave

:)( d N the number of allowed standing wave between and +d

d c a dn d N

d c a dn c a n

)/4(2)(

)/2()/2(

two polarization states

n 0

))(/2( d c a d

)/2( c a d


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for three-dimensional cavity

d c a dr c a r )/2()/2(

the volume of concentric shell dr r r

d c

V d c

a dr r d N

d c

a d

c

a v

c

a dr r

23

23

32

23222

884812)(

)2

(4)2

()2

(44

The number of allowed electromagnetic standing wave in 3D

Proof:

nodalplanes

)2sin()/2sin(),(

)2sin()/2sin(),(

)2sin()/2sin(),(

2/cos)2/(

2/cos)2/(

2/cos)2/(

0

0

0

t z E t z E

t y E t y E

t x E t x E

z z

y y

x x

z

y

x

propagation

direction

/2

/2


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for nodes:

.....3,2,1,/2,,0

.....3,2,1,/2,,0

.....3,2,1,/2,,0

z z z

y y y

x x x

n n z a z

n n y a y

n n x a x

222

2222222

/2

)coscos(cos)/2(

cos)/2(,cos)/2(,cos)/2(

z y x

z y x

z y x

n n n a

n n n a

n a n a n a

d c a dr c a n n n r

r a c n n n a c c

z y x

z y x

)/2()/2(

)2/()2/(/

222

222

d c a d c a d N

d N dr r dr r dr r N 2323

22

)/(4)/2)(2/()(

)(2/4)8/1()(

considering two polarization state

d c V d N 23)/1(42/)(

:/8)( 32 c N Density of states per unit volume per unit frequency


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the law of equipartition energy:

For a system of gas molecules in thermal equilibrium at temperature T,

the average kinetic energy of a molecules per degree of freedom is kT/2,

is Boltzmann constant.K joul e k o /1038.1 23

average total energy of each standing wave :KT KT

2/2 the energy density between and +d:

kTd c

d T 3

28)( Rayleigh-Jeans blackbody radiation

ultraviolet catastrophe

)()4/()( T T c R


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1.4 Plancks theory of cavity radiation

),( T Plancks assumption: and 0,0

kT

the origin of equipartition of energy:

Boltzmann distribution kT e P kT /)( /

:)( d P probability of finding a system with energy between and +d

kT

kT e kT e kT kT

d kT

e d P

e kT kT

d kT

e d P

d P

d P

kT kT

kT

kT

kT

])(|)([1

)(

1|)(1

)(

)(

)(

0

/0

/

0 0

/

0/

0

/

0

0

0


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Plancks assumption: ..............4,3,2,,0 kT kT ,

kT kT ,

kT kT ,

kT 0(1) small

(2) large large 0

s joul h

h

34

1063.6 Planck constant

Using Plancks discrete energy to find

kT h

e

e n kT

e kT

e kT

nh

P

p

n nh

n

n

n

n

n

kT nh

n

kT nh

n

n

/

1)(

)(

......3,2,1,0,

0

0

0

/

0

/

0

0


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0

0

0

0

0

0

0

ln

n

n

n

n

n

n

n

n

n

n

n

n

n

n

e

e n

e

e d

d

e

e d

d

e d d

00

ln]ln[n

n

n

n e d

d h e

d

d kT

1132

32

0

)1()1(.......1

.....1

e X X X X

e e e e

e X

n

n

11)

1

1(

)]1ln([)()1ln(

/

1

kT h e h

e

h e

e h

e d

d h e

d

d h

01

/1

/

/

h e kT h

kT kT h e kT h

kT h

kT h


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energy density between and +d:1

8)( /3

2

kT hT

e

h

c

1

18)()()(

)()(

/52 kT hc T T T

T T

e

hc c

d

d

d d

Ex: Show )()4/()( T T c R

dA

dV

r 22 4

cos

4

r

dA

r

r Ad solid angle expanded by dA is

spectral radiancy:

)(4

sin4

cos)(

)/()4

cos()()(

2220

2/

0

2

0

2

T

t c

T

T T

c

dr r t r

d d

t dAr

dAdV R


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Ex: Use the relation between spectral radiancy

and energy density, together with Plancks radiation law, to derive

Stefans law

d cd R T T )()4/()(

32454 15/2, h c k T R T

44

3

4

2

0

3

3

4

2

0 /

3

200

15

)(2

1

)(21

2)(

4

)(

T h

kT

c

dx e

x

h

kT

c

d

e

h

c

d c

d R R

x

kT h T T T

15/)1/(

/

4

0

3 dx e x

kT h x

x

32

45

152

h c k


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Ex: Show that 15/)1( 410

3 dx e x x

dy e y n

dx e x dx e e x I

e e e e

dx e e x dx e x I

y

n n

x n

n

nx x

n

nx x x x

x x x

0

3

04

00

)1(3

00

3

0

21

1

0

31

0

3

)1(

1

.....1)1(

)1()1(

Sety x n e e n y x n dy dx x n y )1(33 ,)1/()1/()1(

1 40 4

0

3

16

)1(

16

6

n n

y

n n I

dy e y by consecutive partial integration

?1

14

n n

90

1148

18

5)(

6

1)(

4

1

4

1

4

1

22

444

2

12

2

n n n

x

n

x

n n n x F

n x F :F Fourier series expansion


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Ex: Derive the Wien displacement law ( ),T max ./2014.0max k hc T

15

0)1(

50

)(

18

)(

2/

/

/

/5

x

kT hc

kT hc

kT hc T

kT hc T

e x

e

e

kT

hc

e d

d

e

hc

kT hc x /

x e y x

y 21 ,51

Solve by plotting: find the intersection point for two functions

5/11 x y

x e y 2

T max

5

Y

X

intersection points:965.4,0 x x

k hc T /2014.0max


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1.5 The use of Plancks radiation law in

thermometry

(1) For monochromatic radiation of wave length the ratio of the spectral

intensities emitted by sources at and is given byK T o 1 K T o

2

1

12

1

/

/

kT hc

kT hc

e

e

:

:

2

1

T

T standard temperature ( Au )

unknown temperature

C T o melting 1068

(2) blackbody radiation supports the big-bang theory. K o

3

optical pyrometer


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1.6 Plancks Postulate and its implication

Plancks postulate: Any physical entity with one degree of freedom whose

coordinate is a sinusoidal function of time

(i.e., simple harmonic oscillation can posses

only total energynh

Ex: Find the discrete energy for a pendulum of mass 0.01 Kg suspended

by a string 0.01 m in length and extreme position at an angle 0.1 rad.

295

333334

5

102105

10)(106.11063.6

)(105)1.0cos1(1.08.901.0)cos1(

sec)/1(6.11.08.9

21

21

E

E J h E

J mg mgh

l g

The discreteness in the energy is not so valid.

bab 1 intorductions and planck theory

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