Bab 1 Intorductions and Planck Theory
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Transcript of 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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0. Prelude -- Development of
Classical Physics and Dark Clouds
(before 20th century)
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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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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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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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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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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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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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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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Chapter 1 Thermal radiation and Plancks postulate
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.