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JEE MainPhysicsDual Nature of Matter

The variation of de Broglie wavelength ( ) versus 1 K (where K is the kinetic energy) is plotted for an electron, a proton, and an -particle. The plots are straight lines passing through the origin, labelled A, B, and C. If line A is the steepest and line C is the least steep, identify which particle corresponds to line A, line B, and line C respectively.

Options

  1. AA - -particle, B - proton, C - electron
  2. BA - proton, B - electron, C - -particle
  3. CA - electron, B - proton, C - -particle
  4. DA - electron, B - -particle, C - proton

Correct answer

C. A - electron, B - proton, C - -particle

Step-by-step solution

The de Broglie wavelength is given by = h 2mK . This can be written as = ( h 2m ) 1 K . For a graph of versus 1 K , the slope of the straight line is h 2m . The slope is inversely proportional to the square root of the mass of the particle. Since the order of masses is m_e Slope _p > Slope _ . Given that line A is the steepest and line C is the least steep, line A corresponds to the particle with the smallest mass (electron), line B to the proton, and line C to the particle with the largest mass ( -particle). Answe

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