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NEETPhysicsDual Nature of Matter

An electron and a photon have the same energy E . Which of the following correctly describes the shape of the graph showing the variation of the ratio of the de Broglie wavelength of the electron to that of the photon ( _e / _ ph ) with respect to their energy E ?

Options

  1. AA straight line passing through the origin
  2. BA rectangular hyperbola
  3. CA parabolic curve opening towards the positive energy ( E ) axis
  4. DA parabolic curve opening towards the positive ratio ( _e / _ ph ) axis

Correct answer

C. A parabolic curve opening towards the positive energy ( E ) axis

Step-by-step solution

For an electron, the de Broglie wavelength is given by: _e = h p_e = h 2mE For a photon, the energy is related to its wavelength by E = hc _ ph , which gives: _ ph = hc E The ratio of their wavelengths is: _e _ ph = h 2mE hc E = 1 c E 2m Let y = _e _ ph and x = E . The relation becomes: y = k x (where k = 1 c 2m is a constant) Squaring both sides gives y^2 = k^2 x . This equation represents a parabola that opens towards the positive x -axis. Therefore, the graph is a parabolic curve opening towards the positive ene

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