Answer :

In any collision of electron and photon the collision will be elastic.

Energy and momentum will be conserved.


Energy of photon = .(λ is wavelength of photon)


Momentum of photon (p)=


Rest mass energy of electron =.(is the rest mass of electron)


Energy of electron after collision =(m is relativistic mass of electron)


Where ‘c’ is speed of light.


By use of conservation of energy,



Initial energy is sum of photon energy and electron energy


Initial photon energy = pc, rest mass of photon is zero therefore its rest mass energy is zero.


Initial electron energy = rest mass energy of it =


Final energy = energy of electron as it gains velocity. is its relativistic energy, when electron moves with momentum p.


By applying the conservation of energy, we get


=


Squaring both side and solving.


Solving this we get vanish.


it is not possible for a photon to be completely absorbed by a free electron.


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