MHT CET202527 Apr 2025Evening ShiftPhysicsDual Nature of MatterActual
If E_p and E_e represent kinetic energy of photon and electron respectively. If de-Broglie wavelength _p of a photon is twice the de-Broglie wavelength _e of electron, then E_e / E_p is (Speed of electron = C 100 , where 'C' is the velocity of light)
Options
- A2 10⁻²
- B1 10⁻²
- C4 10⁻²
- D8 10⁻²
Correct answer
A. 2 10⁻²
Step-by-step solution
The ratio E_e / E_p is derived from the kinetic energies of an electron and photon sharing equivalent de-Broglie wavelengths, with the electron moving at v_e = C/100 . For a photon, the de-Broglie wavelength gives momentum p_p = E_p/C , so E_p = hC/ _p . For the electron, p_e = m_e v_e = h/ _e , and its kinetic energy is E_e = 1 2 m_e v_e^2 . Substituting, E_e = 1 2 (h/ _e) v_e . The ratio becomes: E_e E_p = 1 2 v_e C _p _e Given _p = 2 _e and v_e = C/100 , substitution yields: E_e E_p = 1 2 1 100 2 = 1 100 Final A