AP EAMCET201920 Apr 2019Evening ShiftPhysicsDual Nature of MatterActual
An electron of charge e and mass m moving with an initial velocity v₀ i is subjected to all electric field E₀ j . The de-Broglie wavelength of the electron at a time t is (Initial de-Broglie wavelength of the electron .= ₀ )
Options
- A₀
- B₀ 1+ e^2 E₀^2 t^2 m^2 v₀^2
- C₀ 1+ e^2 E₀^2 t^2 m^2 v₀^2
- D₀ (1+ e^2 E₀^2 t^2 m v₀^2 )
Correct answer
C. ₀ 1+ e^2 E₀^2 t^2 m^2 v₀^2
Step-by-step solution
de-Broglie relation of a charged particles, = h m v Velocity of charged particle at time t , v =v₀ i + e E₀ m t j or |v|= v₀^2+ ( e E₀ m t )^2 Hence, = h m v₀^2+ ( e E₀ m t )^2 or gathered = h m v₀ 1+ e^2 E₀^2 t^2 m^2 v₀^2 or = ₀ 1+ e^2 E₀^2 t^2 m^2 v₀^2 ( ₀= h m v₀ ) gathered