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NEETPhysicsDual Nature of Matter

A graph is plotted showing the variation of de-Broglie wavelength ( ) on the y-axis against 1 V on the x-axis, where V is the accelerating potential. The graphs for a proton and an alpha particle are straight lines passing through the origin. What is the ratio of the slope of the line for the proton to that for the alpha particle?

Options

  1. A1 : 2 2
  2. B8 : 1
  3. C2 : 1
  4. D2 2 : 1

Correct answer

D. 2 2 : 1

Step-by-step solution

The de-Broglie wavelength of a particle of mass m and charge q accelerated through a potential difference V is given by: = h 2mqV Rearranging the equation to match the form of a straight line y = mx (where y = and x = 1 V ): = ( h 2mq ) 1 V The slope of the graph is S = h 2mq . Therefore, the slope S 1 mq . For a proton, mass is m_p and charge is e . For an alpha particle, mass is 4m_p and charge is 2e . Taking the ratio of their slopes: S_p S_ = m_ q_ m_p q_p = (4m_p)(2e) (m_p)(e) = 8 = 2 2 The ratio of the slopes

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