Lecture Mod Phys Fall 2014 NPG 2 Black Body
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Transcript of Lecture Mod Phys Fall 2014 NPG 2 Black Body
BLACK BODY RADIATIONBLACK BODY RADIATION
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Black Body RadiationBlack Body Radiation
Black Body :‐ It absorbs all radiation it receivesBlack Body : It absorbs all radiation it receives
Practical Realization A I th l it ith ll t th hPractical Realization: An Isothermal cavity with a small aperture through which radiation from out side can be admitted
ρ(υ) dν = energy per unit volume of cavity is contributedρ(υ) dν energy per unit volume of cavity is contributed by the radiation between ν and ν + d ν
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Black Body RadiationBlack Body Radiation
Black Body :‐ It absorbs all radiation it receivesBlack Body : It absorbs all radiation it receives
Practical Realization A I th l it ith ll t th hPractical Realization: An Isothermal cavity with a small aperture through which radiation from out side can be admitted
ρ(υ) dν = energy per unit volume of cavity is contributed by the radiation between ν and ν + d ν
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Blackbody Radiation Spectrum
Energy densityin the windowυ and υ +d υ
ρ(υ)T=1400 K
T=1800 Kρ(υ)J/m -Hz3
T=1000 K
frequency υ4
Lord Rayleigh- James Jeans LawLord Rayleigh James Jeans LawNumber of independent standing waves in the frequency interval
G (υ) dυ = 8πυ2 dυ / c3According to the theorem of equipartition
L = 2(λ/2)g q p
energy , the average energy per degrees of freedom = ½ kT. Each standing wave originates from oscillating electric charge in the wall and 2 degrees of freedom is associated ith the
ε = kT2 degrees of freedom is associated with the wave . Hence average energy L =λ/2
ε kT
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Ultrasonic Catastrophe
T=1800 K
( )T=1800 K
ρ(υ)
T=1400 KT=1000 K
frequency υ6
ρ(υ) T=1800 K
υ dependence2
frequency υ7
Planck’s Formula
when hυ << kT
Rayleigh Jeans law
when hυ << kT
Rayleigh-Jeans law
when hυ >> kTυ large
8Wien’s law ρ(v) dv = (8πv2/c3 )(hv)e-hv/kT dv
Planck’s Concept of Energy Quantization
14th December, 1900
νhE = νhE =
Max Karl Ernst Ludwig Planck1858‐1947 9
Planck’s postulateAny physical entity whose ``co-ordinate” is oscillating sinusoidally with frequency y can possess only total energies E as integral multiple of
h = Planck’s constant
42Classical
E = 0 10
εn = nhv, n = 0, 1, 2, 3,….r
No. of oscillators with energy εn is proportional to e-εn/ kT
. If there are N oscillators and E be the total energy, the average energy ε = E/N. Let there be No , N1 , N2 ,…Nr
ill h i 0 h 2h h d N Noscillators having energy 0, hv, 2hv ,…,rhv and Nr = No e-rhv/ kT
N = N + N + N + +NN = No + N1 + N2 + … +NrE= 0. No e-0/ kT + No hv. e-hv/ kT +No 2hv.e-2hv/ kT +………+
N rhv e-rhv/ kTNo rhv.e
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N = No (e-0/ kT + e -hv/ kT + e -2hv/ kT +………+ e -rhv/ kT )= N / ( 1- e-hv/ kT ) [ 1+x + x2 + x3 + …= 1 /(1-x) ] No / ( 1 e ) [ 1+x + x + x + … 1 /(1 x) ]
E = No hv. e-hv/ kT (1+ 2e-2hv/ kT +………+ re -(r-1)hv/ kT )
= No hv. e-hv/ kT {1/ (1- e-hv/ kT ) }2 [ 1 + 2x + 3 x2 +.. = 1/(1-x)2 ]
ε = E/N
ε =
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Planck’s FormulaPlanck s Formula
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Wien’s displacement Law
Wien's displacement law states that the wavelength distribution of thermal radiation from a black body at any temperature has essentially the same shape as the distribution at any other temperature except that each wavelength isas the distribution at any other temperature, except that each wavelength is displaced on the graph.
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