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JEE MainPhysicsDual Nature of Matter

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

Options

  1. A1 : 8
  2. B2 : 1
  3. C4 : 1
  4. D8 : 1

Correct answer

D. 8 : 1

Step-by-step solution

The kinetic energy gained by a particle of charge q accelerated through a potential difference V is K = qV . The de Broglie wavelength is given by = h 2mK = h 2mqV . Given that _p = _ , we can equate their denominators: 2m_p q_p V_p = 2m_ q_ V_ Squaring both sides: m_p q_p V_p = m_ q_ V_ For an -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 ratio V_p V_ = 8 1 , or 8 : 1 . Answer: 8 : 1

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