COMPTON SCATTERING

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         COMPTON SCATTERING

 


 

 The scattering of photon of energy hn by an electron rest mass m0 After scattering photon scattered at angle  q  and electron scattered at angle  f . The scattered photon has energy hv¢ and electron have energy E.  

From the conservation of energy

 loss in photon energy = gain in electron energy

 hv - hv¢ = KE

The momentum of photon is given   P=E/c =hv/c
From conservation of momentum in x direction ;    hv+0 =(hv¢/c) cos q + P cos f

 conservation of momentum in y direction ;   0=(hv¢/c)sin q +P sin f

solving above 2 equation, we got  λ’-λ= (1-cosq)

              λ’-λ = λc(1-cosq)    where λc =(h/m0c)=2.46 10-12m

            λ’-λ=∆λ called Compton shift

kinetic energy of recoiling electron is   (K.E)max=|hv - hv¢|

                                                  =hv|1-(v/v¢)|   


        (K.E)max=    





 

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                     BLACK BODY RADIATION

A body which absorbs all the incident electromagnetic radiation regardless frequency and angle of incident

When an object is heated, it radiated electromagnetic energy as result of thermal agitation of electrons in its surface. The intensity of radiation depends on its frequency and on the temperature, the light it emits ranges over the entire spectrum.

 An object in thermal equilibrium with its surrounding radiates as much energy it absorbers. A Black body is perfect absorber as well perfect emitter of radiation

 


Some important observation

1.    1.If T3>T2>T1 then λm1> λm2> λm3 and also Im3>Im2>Im1

G

     Itotal =  σT4      where  σ= Stefen's constant 

                                             σ=5.67*10-8  wm-2k-1  

            U(λ) =I/c        where U(λ)  =spectral energy density

         

U(λ) =        (Planks Radiation Formula)

I(λ,T)=        (Wien’s Distribution Law)

 

 

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Q/ A photon of wavelength λ is incident on a free electron at rest and is scattered in the backward direction. The fractional shift in its wavelength in terms of the compton wavelength λc   of the electron is __________?

 

SOL.       ∆λ = λc(1-cosq)

For fractional shift   ∆λ /λ=λc(1-cosq)/λ

q=  π; ∆λ /λ  =  λc(1-cosπ)/λ=λc/λ

 

 

 

 

Q/ A blackbody at temperature T emits radiation at a peak wavelength  λ. If temperature of the blackbody becomes 4T , the new peak wavelength is _________?

 


    

 

 

Q/ When the temperature of a blackbody is doubled ,the maximum value of its spectral energy density ,with respect to that at initial temperature would become ______?

 

 

Ans.   Itotal =  σT4  =σ(2T)4  =16σT4





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