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NEETPhysicsDual Nature of Matter

An electromagnetic wave of frequency is incident on a photosensitive surface having a negligible work function. If the de-Broglie wavelength of the emitted photoelectrons is _d , what will be the slope of the straight-line graph plotted between ( _d) on the y-axis and ( ) on the x-axis?

Options

  1. A1 2
  2. B-1
  3. C-2
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

From Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectrons is given by: K_ max = h - Since the work function is negligible, K_ max = h . The de-Broglie wavelength of the electron is related to its kinetic energy by: _d = h 2mK_ max Substituting K_ max = h into the equation: _d = h 2mh = ( h 2m )^ 1/2 ^ -1/2 Taking the natural logarithm on both sides: ( _d) = ( ( h 2m )^ 1/2 ) - 1 2 ( ) Comparing this with the equation of a straight line y = mx + c , where y = ( _d) and x = ( )

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