An electron (mass m ) with initival velocity `vecv = v_(0) hati + v_(0) hatj` is the an electric field `vecE = - E_(0)hatk` . It `lambda_(0)` is initial de - Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

Options

A. `(lamda_0sqrt2)/(sqrt(1+(e^2E^2t^2)/(m^2v_0^2)))`
B. `(lamda_0)/(sqrt(2+(e^2E^2t^2)/(m^2v_0^2)))`
C. `(lamda_0)/(sqrt(1+(e^2E^2t^2)/(2m^2v_0^2)))`
D. `(lamda_0)/(sqrt(1+(e^2E_0^2t^2)/(5m^2v_0^2)))`

Answer

D

Explanation

By de-Brogile hypothesis
`lambda =h/(mv)`
`lambda_0 = h/(msqrt5 v_0)" "......(1)`
`lambda. =h/(msqrt(v_0^2 + 4v_0^2 + ((eE_0t)/(m))^2))`
`= h/(msqrt(5v_0^2 + (e^2 E_0^2 t^2)/(m^2)))" "......(2)`
By (1) and (2) `lambda.= (lambda_0)/(sqrt(1+(e^2 E_0^2 t^2)/(5m^2 v_0^2))`