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Blackbody Radiation Boltzman’s Statistis Einstein’s Relation

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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


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