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JEE MainPhysicsDual Nature of Matter

An electron and a photon are given to have the same energy E (kinetic energy for the electron and total energy for the photon). If m is the mass of the electron and c is the speed of light, the ratio of the de-Broglie wavelength of the electron to that of the photon is:

Options

  1. Ac 2m E
  2. B1 c E m
  3. C1 c E 2m
  4. DE 2mc^2

Correct answer

C. 1 c E 2m

Step-by-step solution

The de-Broglie wavelength of an electron with kinetic energy E is given by: _e = h p_e = h 2mE The de-Broglie wavelength of a photon with energy E is given by: _ ph = hc E Taking the ratio of the two wavelengths: _e _ ph = h 2mE hc E = h 2mE E hc _e _ ph = 1 c E 2m Answer: 1 c E 2m

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