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
- A8 : 1
- B1 : 8
- C4 : 1
- 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