An electron (mass m , charge -e ) is projected with an initial velocity v = v₀ i ( v₀ > 0 ) into a region containing a uniform electric field E = E₀ j ( E₀ > 0 ). If the initial de-Broglie wavelength of the electron is ₀ , its de-Broglie wavelength after time t is given by:

Step-by-step solution

Initial de-Broglie wavelength is ₀ = h mv₀ . The force on the electron due to the electric field is F = -e E = -eE₀ j . The acceleration of the electron is a = F m = - eE₀ m j . The velocity of the electron after time t is: v = u + a t = v₀ i - eE₀ m t j The magnitude of the velocity (speed) at time t is: v = v₀^2 + ( eE₀ t m )^2 = v₀ 1 + ( eE₀ t mv₀ )^2 The new de-Broglie wavelength is: = h mv = h m v₀ 1 + ( eE₀ t mv₀ )^2 = ₀ 1 + ( eE₀ t mv₀ )^2 Answer: ₀ 1 + ( eE₀ t mv₀ )^2