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Radyasyonun (Inmn) TabiatIk Teorileri
Tanecik (emisyon)Teorisi
Dalga Teorisi
Newton (1670):
In bir k kaynandan k hzyla (3.108 m/s) herdorultuda yaylan kk madde tanecikleri olduunu ileri
srmtr. Bu teoriye emisyon (salma, yaym) veya tanecikteorisi denir. Bu teoriye gre farkl renklere trl boyuttakitanecikler neden olmaktadr. Ktleleri ok kk hzlar okbyk olduundan bu tanecikler yerekimi etkisi ileyollarndan sapmazlar. Bylece arlkszm gibi hareketettiklerini kabul eden bu teori ile n bir doru zerindeyaylmasnbaarl bir ekilde izah eder.
Ayrca elik bir bilyenin elik bir levha zerinde yansmasgibi nda yansyabileceini aklar. Yine elik bilyelerleyaplan uygun deneylerle n krlmas izahedilebilmektedir.
Huygens (1670):
In dalga tabiatnda olduunu ve dalga yzeyinin btnnoktalarnn elemanter kk dalgacklar meydana getirdiini
dnerek n yansma ve krlma kanunlarn yenidentretmitir.
Newton bu teoriye bir akkan iinde oluandalgalarn nlerinerastlayan engellerin yan kenarlarn dnerek geometrik glgead verilen szmalarn (difraksiyon veya krnm olay)gereke gstererek itiraz etmitir. Bu teori ile n keskinglgeler oluturmasn aklayamamas 1 asr kadar dalgateorisinin gzden dmesine neden oldu.
ngiliz Dr. Young ve Fransz Fresnel (1788-1827) yaptklaralmalarda interferans (giriim) olaylarn ancak dalga teorisiile aklayabildilernk k+nkaranlkolabilecei ancakdalga teorisi ile aklanabilmekteydi.
Ayrca Fresnel k dalgalaryla su dalgalarnn arasndakiglge oluumu(krnm)bakmndan grlen farknkaynandalga boylarnn ok farkl olmasndan kaynaklandn ispatetti. Bylece n dorusal yaylmn baarl bir ekildeaklad. Huygensingrn zor durumda brakan ve gzdendmesine yol aan neden ortadan kaldrlm oldu.
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Krnm Giriim
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Huygens n polarizasyonunu n ses dalgalar gibi boyuna dalgalar olduunudndndenaklayamamt. Ancak Fresnel k titreimlerinin enine olduunu kabul ederekizah etmeyi de baard.
Foucault (Fuko) tarafndan sudaki k hznn deneysel olarak llmesi tanecik teorisinin
btnyle iflasna yol at nk tanecik teorisiyle her ne kadar krlma alarnn oran sabitkalsada youn ortamdaki khznn daha byk olmas gerekmekteydi. Ancak deneyler sudakikhznn havadakinden daha dkolduunugstermitir.
Bylece IIINENNE YAYILAN DALGALAR olduu sonucuna varld.
Maxwell 1861-1864 yllarnda tamamen teorik olarak khzyla hareket eden dalga denklemlerinitrettti. Bu denklemler ayrca n elektrik ve manyetik bileenleri olduunu ve birbirine dikdzlemlerde sins erilerine benzer ekildeyayldklar sonucuna vard.
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1888 ylnda Hertz Maxwellin elektromanyetik dalgalarn bir elektrik titreim devresi kullanaraklaboratuvarnda elde etmi ve bu dalgalarn yansma,krlma, odaklanma, giriim vb. zellikleresahip olduunugstermitir. Ayrca bu dalgalarnhzlarnltnde teorik yoldan bulunan khznaeitolduunu grd.
Artkn dalga tabiatndaolduu 19. yydaphe gtrmez bir gerek olarak kabul edildi. 1900l yllarda bir takm deneylerin klasik fizik kanunlar ve elektromanyetik teoriyleaklanamad grld. O gne kadar elde edilen bilimsel birikim o gn iin yeni olan olaylaraklayamadndan dolayilerkarmayabalad ve o gne kadar kesin doruolduunainanlanfizik kanunlarnn mkemmel olmadnnfarknavarld.
Siyah Cisim Imas
Fotoelektrik OlayCompton Olay aklanamad
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Termal Radyasyon ve Planck Denklemi
Bu blmde klasik fiziinaklayamad baz olaylar ve ilgilideneyler zerinde duracaz.
Bu deneyler sonucu
Inmn kuantl olduu grlmtr!
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_Siyah Cisim Imas_(blackbody radiation veya cavity radiation)
--- Gzlemler ---
Bir metal ubuk stlnca neler olur ?
Scaklk ykseldike renkte nasl bir deiim oluur ?
Bunzen bek alevinin scakl hakknda ne biliyorsunuz ?
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Scak cisimler k yayarlarRenk nce krmz sonra sar sonra daha parlak sarolur
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Cisimler niin ma yapar?
Cisimler atomlardan meydana gelmitir
Mutlak sfrdan yksek scaklktaki btncisimler elektromanyetik ma yaparlars enerjisi
Titreen atomlar ma yaparlar.
Cisimlerin top-yay modeli
Is, molekl hareketlerinin (teleme, dnme, titreim)
ortalama kinetik enerjisinden kaynaklanr
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yaydklar radyasyon daha ksa dalga boyuna kayar(red white blue)
--- Tanmlar---
Siyah cisim:
zerine den btn mkemmel bir ekilde
absorbe eden bir cisimdir. zerine den btn sourduu iin kara grnr veya grnmez (karadelikler gibi..)
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The failures of Classical PhysicsSiyah cisim var mdr?
Nasl yaplabilir ?
T
Ima Gc (R); deal bir siyah cisim olarak dnlen
kk deliin birim alanndan birim zamanda yaylan enerjimiktarnama gc denir. Birimi J/m2.s-1
Enerji Younluu ( ); Siyah cismin boluundaki (cavity)enerji miktarnnboluk hacmine orandr. Birimi J/m3
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Ima nasl gzlemlenir ?
Ima monokromatik mi yoksa polikromatik
midir ?
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Gnein yzey scakl 5800 K ve scak bir odun atei ise yaklak800 oK dir. Cisimler scaklnn 4 kuvveti ile orantl olarak mayapmaktadr.
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Radiated Power from Blackbody When the temperature of a blackbody radiator increases, the overall
radiated energy increases and the peak of the radiation curvemoves to shorter wavelengths. When the maximum is evaluated
from the Planck radiation formula, the product of the peakwavelength and the temperature is found to be a constant.
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod6.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod6.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html -
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Wien yasas:
Experimental observation
As the temperature raised, the peak in the
energy output shifts to shorter
wavelengths. Wien displacement law
Stefan-Boltzmann law
Wihelm Wien2max 5
1cT Kcm44.12 c
4/ aTVE 4TM
mK10.90,2 3max T
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Zero amplitude
at boundary
L
wavelength
=c/ , = # of
cycles per sec
Standing Wave
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Imann klasik fizik yorumuRayleigh-Jeans kanunu
3
28
c
Birim hacimde birim frekanstakimodlarn says:
standing waves originate from harmonically oscillatingcharges in cavity wall
two degrees of freedom (potential and kinetic energy)Average energy per degree of freedom: kT(equipartition)
average energy per standing wave: kTkT212
dc
kTdu
2
3
8)( total energy per unit volume:
Lord Rayleigh
Enerji dalmn aklamak zere ilk ne srlen teoridir veklasik mekaniin enerjinin eblm prensibini kullanmtr.
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Formln tretilmesi
Rayleigh and Jeans kapal bir kavite iindeki enerji younluunu hesaplamak
istediMetal bir kutu iindeki radyasyon gz nne alndnda radyasyonun duran
dalga (kararl dalga) eklinde olmas gerektii bilinmektedir. Ayn zamanda bu
kararl dalgalar ancak belirli bir dalga boylarna sahip olabilirler (belirlifarkl frakanslar)
Belirli bir scaklkta (T=sbt) ile +dfrekanslar aralnda birim hacimdekienerji miktar
ile verilebilir.
hacim
)erji/dalgasayisi)(en(dalga)( dT
dc
VdN
2
3
8)(:sayisidalga
Dalgalarn farkl sayda
olabilecekleri dikkate alnmtr Enerjinin istenen her deerde olabilecei n grlmtr
enerji/dalga: = kT
(enerjinin e blm kanunu kullanldnda )
d
c
dT 3
28)(
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T() ile verilebilir mi ?
= c/olduu bilindiine gre diferansiyeli d = (c/2)d
e eittir. Bylece frekans ve dalga boyu arasnda geiyaplabilir:
T()d = T()d
buradan T() T()d/d T()c/2
elde edilir.Frekansa bal olarak verilen enerji younluu dalga boyuna
balanacak olursa:
dc
c
cd
c
cd
d
c
d
T
T
223
2
23
2
3
2
88)(
8)(
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Teori uzun dalga boylarnda iyi sonular verirken ksa dalga boylarndadeney sonularndan olduka sapmaktadr.
Hatta bu olaya ultraviyole felaketi (Ultraviolet Catastrophe) adverilmitir. nk eer teori doru olsayd. Oda scaklnda soukcisimler bile grnr ve ultraviyole blgede ma yapacaklard. Yanihepimiz kzartmaolacaktk !!
dkTdu4
8)( 4
1
4)(
8
kT
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PlanckKanunu
Energies are limited to discrete value
Quantization of energy
Plancks distribution
At high frequencies approaches the Rayleigh-Jeanslaw
The Plancks distribution also follows Stefan-Boltzmanns Las
Max Planck
,...2,1,0, nnhE
ddE)1(
8/5
kThc
e
hc
kThc
kThce kThc
1....)1()1( /
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blackbody radiation quantum mechanical
average energy per standing wave:
1
/ kThe
h
M. Planck (1900):1
8)(
/
3
3
kThe
d
c
hdu
(fit to the data)
Js10626.6
34h
Plancks constant
energy of a single oscillator: ,...4,3,2,1 nhn
quantization of energy!
Note: both Stefans Law &
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Planck radiation law
blackbody radiation, photons (bosons) in a cubic cavity:standing wave condition in all three directions x,yand z
d
ec
hfGhdu
dc
dG
d
c
Ldg
Lnnn
Ln
kTh
zyx
zyx
/3
3
2
3
2
3
3
2222
,,
18)()()(
8)(
8)(
2
...4,3,2,1,02
(number of standing waves)
(standing waves in cubic cavity)
(density of standing waves)
Note: both Stefans Law &
Wiens Displacement law
Can Be derived from the
Plank formula
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Finding the Blackbody Peak From the Planck radiation formula
the evaluation of the maximum yields Wien's displacement law To find the peak of theblackbody radiation curve, we take the derivative:
Simplifying gives the maximum condition:
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Cavity Modes
A mode for an electromagnetic wave in a cavity must satisfy thecondition of zero electric field at the wall. If the mode is of shorterwavelength, there are more ways you can fit it into the cavity to meet
that condition. Careful analysis by Rayleigh and Jeans showed thatthe number of modes was proportional to the frequency squared.
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Discovery of Cosmic Background Radiation In 1965 Arno A. Penzias and Robert W. Wilson of Bell Laboratories
were testing a sensitive horn antenna which was designed for
detecting low levels of microwave radiation. They discovered a lowlevel of microwave background "noise", like the low level of electricalnoise which might produce "snow" on a television screen. Afterunsuccessful attempts to eliminate it, they pointed their antenna toanother part of the sky to check whether the "noise" was comingfrom space, and got the same kind of signal. Being persuaded thatthe noise was in their instrument, they took other, more
sophisticated steps to eliminate the noise, such as cooling theirdetector to low temperatures. Finding no explanations for the origin of the noise, they finally
concluded that it was indeed coming from space, but that it was thesame from all directions. It was a distribution of microwave radiationwhich matched a blackbody curve for a radiator at about 2.7 Kelvins.
After all their efforts to eliminate the "noise" signal, they found that agroup at Princeton had predicted that there would be a residualmicrowave background radiation left over from the Big Bang andwere planning an experiment to try to detect it. Penzias and Wilsonwere awarded the Nobel Prize in 1978 for their discovery.
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Thermometry
Planck law gives the radiancy as a function ofTand
Resistance is adjusted until filament is invisible against source background
IfT1 is taken as a reference, T2 can be determined
1)/exp(
1)/exp(
2
1
kThc
kThcR
For monochromatic radiation of wavelength , the ratio of spectral intensities
is given by
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Heat Capacities
Dulong Petits Law
The molar heat capacities of monoatomic solids are the same , close
to 25 J/mol. K
Can be justified using classical mechanics
Mean energy of an atom oscillates about its mean position of solid iskT
Unfortunately, at low T the value
approaches to zero
RTkTNU Am 33
KJ/mol9.243
R
T
UC
V
mv
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Einstein and Debye Formula
Einstein used the hypothesis that energy of
oscillation is confined to discrete value
Debye later refined Einstein formula taking into
account that atoms are not oscillating at the same
frequency.
23RfCv
12/
2/
T
T
E
E
E
e
e
Tf
RfCv 3 dxe
exTf
T
x
x
D
D
/
0 2
43
)1(3
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Einstein and Debyes Theory
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overviewstatistical distributions general considerations
Maxwell-BoltzmannBose-EinsteinFermi-Dirac
Maxwell-Boltzmann statisticsMaxwell-Boltzmann distributionenergies in an ideal gas
equipartition of energyquantum statistics
fermions and bosonsBose-Einstein and Fermi-Dirac distribution
comparison of the three statistical distributions
applicationsPlanck radiation lawspecific heats of solidsfree electrons in a metaldying stars
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specific heats of solids
question: internal energy of solids, specific heat
vc : energy needed to raise T of 1 kmol of solid by 1 K at constant V
internal energy resides in vibrations of the solids constituents
vibration of classical 1-D harmonic oscillator:
solid: 3 perpendicular modes of vibration 3 harmonic oscillators
total energy of a solid:
kT
RTkTNE 33 0
RT
Ec 3
V
v
(Dulong Petit)
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specific heats of solids
problem: deviation from Dulong-Petit!
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specific heats of solids
solution by Einstein: use average energy of a harmonic oscillator
1/
kTh
e
h
Ee
NhN
kTh
1
33
/
for N oscillators and 3 dimensions:
2/
/2
V
v)1(
3
kTh
kTh
e
e
kT
hR
T
Ec
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specific heats of solids
refinement by Debye: elastic standing waves of the whole body
quantum of acoustic energy phonons
number of possible standing waves in a body equals 3N
phonons are bosons
BE statistics lead to good agreement with experimentalspecific heats
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overviewstatistical distributions general considerations
Maxwell-BoltzmannBose-EinsteinFermi-Dirac
Maxwell-Boltzmann statisticsMaxwell-Boltzmann distributionenergies in an ideal gas
equipartition of energyquantum statistics
fermions and bosonsBose-Einstein and Fermi-Dirac distribution
comparison of the three statistical distributions
applicationsPlanck radiation lawspecific heats of solidsfree electrons in a metaldying stars
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free electrons in a metal
about 1 free electron/atom in a metal3 additional degrees of freedom
specific heat should be
RRRRT
E
c 32
9
2
3
2
6
Vv
why do the electrons not contribute to the specific heat?
dhmdg 3
2/3V28
)(
(number of electron states)
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free electrons in a metal
deh
mdn
kTF
1
1V28)(
/)(3
2/3
(electron energy distribution)
V
V8
32
3/22
NNmhF
: electron density
Fermi energy
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free electrons in a metal
T=0
T>>0
EF
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free electrons in a metal
n
n
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free electrons in a metal
only electrons close close to F contribute to cVelectrons more than kT from F cannot be excitedstates above the low lying electrons are already filled
RkT
c
F
e
2
2
v
low T: cve becomes important, since cDebye scales with T3
high T: cve continues to rise when cDebye already reached 3R
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overviewstatistical distributions general considerations
Maxwell-BoltzmannBose-EinsteinFermi-Dirac
Maxwell-Boltzmann statisticsMaxwell-Boltzmann distributionenergies in an ideal gas
equipartition of energyquantum statistics
fermions and bosonsBose-Einstein and Fermi-Dirac distribution
comparison of the three statistical distributions
applicationsPlanck radiation lawspecific heats of solidsfree electrons in a metaldying stars
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