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Cool goIITian

Joined:	5 Jan 2007
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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.

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edison

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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

hν + 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).

edison

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Joined: 19 Oct 2006

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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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