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Question
Show that it is not possible for a photon to be completely absorbed by a free electron.
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Solution
When an electron undergoes an inelastic collision with a photon, we can apply the principle of conservation of energy to this collision. So,
`pc + m_eC^2 = sqrt(p^2C^2 + m_e^2C^4) ....(1)`
Here, h = Planck's constant
c = the speed of light
me = rest mass of electron
pc = energy of the photon
Squaring on both side of equation (1),
`(pc + m_eC^2)^2 = p^2C^2 + m_e^2C^4`
`⇒ p^2C^2 + m_e^2C^4 + 2(pc)(m_eC^2) = p^2C^2 + m_e^2C^4`
`⇒ 2(pc)(m_eC^2) = 0 or pc = 0 ("as" 'm' and 'c' "are non zero")`
This gives vanishing energy of photon which is not possible.
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