MHT CET202526 Apr 2025Evening ShiftPhysicsDual Nature of MatterActual
Let E_e and E_p represents kinetic energy of electron and photon respectively. If de-Broglie wavelength of a photon is twice the de-Broglie wavelength of an electron then E_p / E_e is (speed of electron =C / 100 where C is the velocity of light)
Options
- A10
- B10^2
- C10^3
- D10^4
Correct answer
B. 10^2
Step-by-step solution
De Broglie wavelengths: For the electron and photon, _e = h / p_e and _p = h / p_p , respectively. Wavelength relationship: Given _p = 2 _e , substitution yields h / p_p = 2h / p_e , so p_e = 2p_p . Momentum expressions: For the photon, p_p = E_p / c . For the electron, p_e = m_e v_e . Substitute and simplify: m_e v_e = 2 (E_p / c) Solving for photon energy, E_p = (m_e v_e c) / 2 . Electron kinetic energy: E_e = (1/2) m_e v_e^2 . Energy ratio: E_p E_e = (m_e v_e c)/2 (1/2) m_e v_e^2 = c v_e . Given electron speed: