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JEE MainPhysicsDual Nature of Matter

Graphs of de Broglie wavelength ( ) versus 1 V are plotted for a proton and an particle accelerated from rest, where V is the accelerating potential. Both plots are straight lines passing through the origin. The ratio of the slope of the graph for the proton to the slope of the graph for the particle is :

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 charged particle accelerated from rest through a potential difference V is given by: = h p = h 2mqV This can be rewritten as: = ( h 2mq ) 1 V For a graph of versus 1 V , the slope S is: S = h 2mq The ratio of the slope for the proton to that for the particle is: S_p S_ = h 2m_pq_p h 2m_ q_ = m_ q_ m_p q_p We know that for an particle, m_ = 4m_p and q_ = 2q_p . Substituting these values: S_p S_ = 4m_p 2q_p m_p q_p = 8 = 2 2 Thus, the required ratio is 2 2 :1 . Answer: 2 2 :1

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