An electron of mass m is moving in an electric field E = -2E₀ i ( E₀ = constant > 0 ), with an initial velocity V = v₀ i ( v₀ = constant > 0 ). If ₀ = h 4mv₀ , its de Broglie wavelength at time t is __________. ( e = charge of electron)

Step-by-step solution

The force experienced by the electron in the electric field is given by F = q E . Since the charge of an electron is -e and the electric field is E = -2E₀ i , the force is: F = (-e)(-2E₀ i ) = 2eE₀ i The acceleration of the electron is: a = F m = 2eE₀ m i Using the first equation of motion, the velocity of the electron at time t is: v (t) = V + a t = (v₀ + 2eE₀ m t ) i The de Broglie wavelength of the electron at time t is: = h m| v (t)| = h m (v₀ + 2eE₀ m t ) We are given that ₀ = h 4mv₀ , which implies h = 4mv₀ ₀