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NEETPhysicsDual Nature of Matter

A proton and an alpha particle are accelerated from rest through potential differences V_p and V_ , respectively. If their associated de-Broglie wavelengths are found to be equal, what is the ratio of V_p to V_ ?

Options

  1. A8 : 1
  2. B1 : 8
  3. C4 : 1
  4. D2 : 1

Correct answer

A. 8 : 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 2mqV Given that _p = _ , we have: h 2m_p q_p V_p = h 2m_ q_ V_ Squaring both sides and rearranging the terms gives: m_p q_p V_p = m_ q_ V_ We know that for an alpha particle, the mass is m_ = 4m_p and the charge is q_ = 2q_p . Substituting these values into the equation: m_p q_p V_p = (4m_p)(2q_p)V_ V_p = 8V_ Thus, the required ratio V_p V_ = 8 1 , or 8 : 1 . Answer: 8 : 1

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