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) λ_{0}/(1 + eE_{0}t/mv_{0})

(b) λ_{0}(1 + eE_{0}t/mv_{0})

(c) λ_{0}

(d) λ_{0}t

Ans: (a)

Sol: Initial wavelength , λ_{0} = h/mv_{0}

Acceleration of electron , a = eE_{0}/m

v = u + at ⇒ v = v_{0} + (eE_{0}/m )t

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

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

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