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JEE MainPhysicsDual Nature of Matter

An electron and a photon have the same kinetic energy. If a graph is plotted with the natural logarithm of the photon's wavelength, ( _p) , on the y -axis and the natural logarithm of the electron's de Broglie wavelength, ( _e) , on the x -axis, what will be the slope of the resulting straight line?

Options

  1. A1
  2. B2
  3. C1 2
  4. D4

Correct answer

B. 2

Step-by-step solution

The de Broglie wavelength of an electron with kinetic energy E is given by: _e = h 2mE Squaring both sides, we get: E = h^2 2m _e^2 For a photon, the energy E is related to its wavelength _p by: E = hc _p Since both have the same energy, we can equate the expressions for E : hc _p = h^2 2m _e^2 _p = ( 2mc h ) _e^2 Taking the natural logarithm on both sides: ( _p) = 2 ( _e) + ( 2mc h ) Comparing this with the equation of a straight line y = mx + c , where y = ( _p) and x = ( _e) , the slope m is 2 . Answer: 2

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