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NEETPhysicsDual Nature of Matter

A photon and an electron (mass m ) are found to have the exact same de Broglie wavelength . If c is the speed of light and h is Planck's constant, the ratio of the energy of the photon to the kinetic energy of the electron is:

Options

  1. A2mc h
  2. Bh 2mc
  3. C2m hc
  4. Dc 2m

Correct answer

A. 2mc h

Step-by-step solution

The energy of a photon in terms of its wavelength is given by: E_ photon = hc For an electron of mass m , the de Broglie wavelength is = h p , so its momentum is p = h . The kinetic energy of the electron is: E_ electron = p^2 2m = h^2 2m ^2 Taking the ratio of the energy of the photon to the kinetic energy of the electron: E_ photon E_ electron = hc h^2 2m ^2 E_ photon E_ electron = hc 2m ^2 h^2 = 2mc h Answer: 2mc h

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