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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