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NEETPhysicsDual Nature of Matter

An electron of mass m and a photon have the same de Broglie wavelength . The ratio of the kinetic energy of the electron to the energy of the photon is : (Take c as the speed of light and h as Planck's constant)

Options

  1. Ah 2mc
  2. B2mc h
  3. Ch mc
  4. D1

Correct answer

A. h 2mc

Step-by-step solution

Since the electron and the photon have the same de Broglie wavelength , they possess the same linear momentum p . The momentum is given by: p = h The kinetic energy of the electron E_e is related to its momentum by: E_e = p^2 2m = h^2 2m ^2 The energy of the photon E_ ph is related to its momentum by: E_ ph = pc = hc Taking the ratio of the kinetic energy of the electron to the energy of the photon: E_e E_ ph = h^2 2m ^2 hc = h 2mc Answer: h 2mc

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