JEE Main202524 Jan 2025Morning ShiftPhysicsDual Nature of MatterActual
An electron of mass ' m ' with an initial velocity v = v ₀ i ( v ₀ 0 ) enters an electric field E =- E _ o k . If the initial de Broglie wavelength is ₀ , the value after time t would be
Options
- A₀ 1+ e ^2 E ₀ ^2 t ^2 ~m ^2 v ₀ ^2
- B_ o 1+ e ^2 E ₀^2 t ^2 ~m ^2 v _ o ^2
- C₀ 1- e ^2 E _ o ^2 t ^2 ~m ^2 v _ o ^2
- D₀
Correct answer
A. ₀ 1+ e ^2 E ₀ ^2 t ^2 ~m ^2 v ₀ ^2
Step-by-step solution
aligned & v = v ₀ i - E ₀ e m t k & | v |= v ₀^2+ E ₀^2 e ^2 t ^2 ~m ^2 & ₀= h mv ₀ & ^ = h mv ₀ 1+ E ₀^2 e ^2 t ^2 v ₀^2 ~m ^2 & ^ = ₀ 1+ E ₀^2 e ^2 t ^2 v ₀^2 ~m ^2 aligned