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NEETPhysicsDual Nature of Matter

An electron (mass m , charge e ) is accelerated from rest through a potential difference V . A photon has an energy exactly equal to the kinetic energy acquired by this electron. The ratio of the momentum of the photon to the momentum of the electron is: ( c is the speed of light)

Options

  1. Ac 2m eV
  2. B1 c eV 2m
  3. C1 c 2m eV
  4. D1 c eV m

Correct answer

B. 1 c eV 2m

Step-by-step solution

The kinetic energy acquired by the electron when accelerated through a potential difference V is: E = eV The momentum of the electron is related to its kinetic energy by: p_ electron = 2mE = 2meV The photon has the same energy E = eV . The momentum of a photon is given by: p_ photon = E c = eV c Taking the ratio of the momentum of the photon to the momentum of the electron: p_ photon p_ electron = eV c 2meV p_ photon p_ electron = 1 c (eV)^2 2meV = 1 c eV 2m Answer: 1 c eV 2m

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