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BLACKBODY
RADIATIO NBO LTZM AN’S STATISTISEINSTEIN’S RELATIO N
A & B CO -EFFICIENTSBy Muhammad Abubakar Farooq
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Blackbody Radiatio
▪ The term black body was introduced by Gustav Kirchhin 18!"
▪ Black#body radiation is also called complete radiationtemperature radiation or thermal radiation or cavityradiation"
▪ $t re%ers to an ob&ect or system which absorbs all radiincident u'on it and re#radiates ener(y which ischaracteristic o% this radiatin( system only) not de'enu'on the ty'e o% radiation which is incident u'on it"
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Blackbody Radiatio L!"!l
▪ The radiation level o% a blackbody only de'ends on itstem'erature and is well#known throu(h the *lanck+s law
▪ The amount o% radiations emitted in a (iven %requencyran(e should be 'ro'ortional to the number o% modes iran(e"
▪ *lanck,s law states that
-here
▪ I.ν)T / is the ener(y 'er unit time .or the 'ower/ radiateunit area o% emittin( sur%ace in the normal direction 'esolid an(le 'er unit %requency by a black body at
tem'erature T ) also known as s'ectral radiance"
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Blackbody Radiatio# ad T!$ %!at'! The radiation hass'ectrum and intede'ends only on to% the body"
As the tem'eratuthe 'eak o% the blradiation curve mintensities and lonwavelen(ths"
A black#body at rotem'erature a''eviewed in the dar &ust %aintly visible
sub&ectively a''ethou(h its ob&ectis'ectrum 'eaks inran(e"
-hen it becomes a''ears dull red"
As its tem'eratur%urther it eventuablindin(ly brilliant
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A%%licatio# o( Blackbody Radiatio
▪ The main a''lications are o% course $ sensorscalibration and their s'eci0cations measurement
▪ Blackbodies are also used as o'tical re%erence sourc%or optical sensors.
▪ 2'tical Fibre Tem'erature 3ensor are based on the'rinci'le o% Blackbody adiation"
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Bolt)$ a’# Stati#tic#
▪
$n statistical mechanics) Maxwell–Boltzmann statisticsthe avera(e distribution o% non#interactin( material 'articvarious ener(y states in thermal equilibrium"
▪ $t is a''licable when the tem'erature is hi(h enou(h or thdensity is low enou(h to render quantum efects ne(li(ibl
▪ Ma4well5Bolt6mann statistics can be derived in various st
mechanical thermodynamic ensembles7* The (rand canonical ensemble) e4actly"
* The canonical ensemble) e4actly"
* The micro canonical ensemble) but only in the thermodynamic limit
▪ $n each case it is necessary to assume that the 'articles ainteractin() and that multi'le 'articles can occu'y the sam
and do so inde'endently"
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M at+!$ atical Fo$
▪ The e4'ected number o% 'articles with ener(y %or Ma4well5Bo
statistics is
where
▪ is the ith ener(y level
▪ is the number o% 'articles in the set o% states with ener(y
▪ is the de(eneracy o% ener(y level i) that is) the number o% states
▪ is the chemical 'otential
▪ T is absolute tem'erature
▪ N is the total number o% 'articles
▪
Z is the 'artition %unction
▪
M ll B lt
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A%%licatio# o( Bolt)$ a Stati#tic#
Ma4well#Bolt6mstatistics are usrelate the relat'o'ulation o% aener(y levels wused in 'o'ulatinversion"
Ma4well5Bolt6mstatistics are usderive the Ma4Bolt6manndistribution .%orideal (as o% cla'articles in a thdimensional bo
Fi(ure shows thdistribution o% 's'eed %or 1!:o4y(en 'article;1!!)
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Ei#t!i’# R!latio# ad Co!( (ici!t# ,A&
▪ $n 1>1) Albert ?instein 'ro'osed that there are three 'rocess
occurrin( in the %ormation o% an atomic s'ectral line"
▪ The three 'rocesses are re%erred to as s'ontaneous emissionstimulated emission) and absor'tion"
▪ -ith each is associated an ?instein coe@cient which is a meo% the 'robability o% that 'articular 'rocess occurrin( by an atmolecule"
▪ These coe@cients are called ?instein+s =oe@cient and the rebetween these coe@cients are called ?instein+s elations"
▪ The ?instein A coe@cient is related to the rate o% s'ontaneouemission o% li(ht
▪ The ?instein B coe@cients are related to the absor'tion andstimulated emission o% li(ht"
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.i#toical Cot!/t
▪ $n 1>1) ?instein considered a (as molecules in thermodyn
equilibrium with electroma(netic radiation"
▪ By considerin( two such levels ?< and ?1 with ?< ?1) ?in'ostulated that the number o% transitions) in time dt) %or thener(y level ?< to the lower state ?1 will consist o% two com
* The 0rst com'onent will arise %rom the s'ontaneous &um' %rom ?< to o% transitions will be (iven by the term A
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Cot’d
▪ 3olvin( %or we (et7
▪ Bolt6mann told us that the number o% 'articles in thelevel will be 'ro'ortional to the density o% states timeBolt6mann %actor7
▪ Esin( this result %or 1 and < in the 'revious result)
▪ From -ien,s dis'lacement we conclude that ?
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0it# o( Ei#t!i’# Co!( (ici!t#
▪
The ?instein relations7* Connect properties of the atom. Must hold even out ofthermodynamic equilibrium.
* Allow determination of all the coecients iven the valone of them.
▪ The units o% ?instein+s A coe@cient is
* is the transition 'robability 'er unit time
▪ The units o% ?instein+s B coe@cients are
* sr is solid an(le and is dimensionless
▪
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uestionHH
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Thank Iou