An electron (mass m) with an initial velocity v = vo i ̂(vo >0) is in an electric field E= -Eo i ̂ (Eo = constant > 0)…..

Q. An electron (mass m) with an initial velocity $ v = v_o\hat{i} (v_o > 0)$ is in an electric field $E = -E_o\hat{i} (E_o =constant > 0)$ . Its de Broglie wavelength at time t is given by

(a) λ₀/(1 + eE₀t/mv₀)

(b) λ₀(1 + eE₀t/mv₀)

(c) λ₀

(d) λ₀t

Ans: (a)

Sol: Initial wavelength , λ₀   = h/mv₀

Acceleration of electron , a = eE₀/m

v = u + at ⇒ v = v₀ + (eE₀/m )t

Wavelength , $\large \lambda = \frac{h}{m v} = \frac{h}{m (v_o + \frac{eE_o}{m} t)}$

$\large \lambda = \frac{h}{m v_o  (1 + \frac{eE_o}{m v_o} t)}$

$\large \lambda = \frac{\lambda_o}{ (1 + \frac{eE_o}{m v_o} t)}$