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Modern Physics

Cool goIITian

 Joined: 5 Jan 2007 Post: 36
8 Sep 2008 13:49:10 IST
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Complete Photon absorption
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Show that an isolated electron cannot absorb a photon completely.

Promise a salute

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Joined: 19 Oct 2006
Posts: 7797
8 Sep 2008 20:31:03 IST
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The proof for a photon cannot transfer all its energy to an isolated electron is a follows

By Conservation of Energy

+  m0C2 = mC2                                ...(1)

Where m0 = Rest mass of an electron

m = Relativistic mass of electron after complete photon absorption

C = Speed of light in vacuum

m = γm0

Here γ2 = 1/ (1 - β2) or γ = 1/ (1 - β2)1/2

and  β = V/C

Here V = velocity of electron after complete absorption of photon

Equation (1) is written as

hν = m0C2 (γ – 1)                     ...(2)

By conservation of momentum

hν/C = mV = γm0 βC

or hν = γm0 βC2                       ...(3)

Equating (2) & (3) we obtain

m0C2 (γ – 1) = γm0 βC2

or (γ – 1)= γβ

or  1/ (1 - β2)1/2  - 1 = β/(1 - β2)1/2

Solving which we obtain

β(1-β) = 0

Hence either  = 0, and the electron is at rest after the interaction which is not possible as conservation of momentum will not hold good otherwise.

or β = 1 or V = C, i.e. the electron is moving with the speed of light. This is again impossible.

Consequently simultaneous conservation of energy & momentum requires the presence of a third body (namely, the nucleus).

Forum Expert
Joined: 19 Oct 2006
Posts: 7797
8 Sep 2008 20:32:21 IST
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Thats why photo electric effect (complete absorption of photon by an electron in an atom) occurs with bound electron but not free electron.

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