An electron (mass m ) with an initial velocity v = v 0 hat i ( v 00) is moving in an electric field E =- E 0 hat i ( E 00) where E 0 is constant. If at t =0 de Broglie wavelength is λ0=( h / mv ), then its de Broglie wavelength after time t is given by

Question

An electron (mass m ) with an initial velocity v = v 0 hat i ( v 0>0) is moving in an electric field E =- E 0 hat i ( E 0>0) where E 0 is constant. If at t =0 de Broglie wavelength is λ0=( h / mv ), then its de Broglie wavelength after time t is given by (A) λ0 (B) λ0(1+( eE 0 t / mv 0)) (C) λ0 t (D) (λ0/(1+( eE 0 t ) mv 0))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6186dea49cac07fe3e6a24189eacbda7-.png" /> E =- E 0 hat i λ0=( h / mv 0) v = v 0+( e E 0 t / m ) λ=( h / mv )=( h / m ( v 0+( eE 0) m t )) λ prime=( h / mv 0(1+( eE ) mv t )) λ prime=(λ0/(1+( eE 0) mv 0 t ))

Q. An electron (mass $m$ ) with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ is moving in an electric field $E = - E_{0} \hat{i} (E_{0} > 0)$ where $E_{0}$ is constant. If at $t = 0$ de Broglie wavelength is $λ_{0} = \frac{h}{m v}$ , then its de Broglie wavelength after time $t$ is given by

$λ_{0}$

$λ_{0} (1 + \frac{e E _{0} t}{m v _{0}})$

$λ_{0} t$

$\frac{λ _{0}}{( 1 + \frac{e E _{0} t}{m v _{0}} )}$

$E = - E_{0} \hat{i}$
$λ_{0} = \frac{h}{m v _{0}}$
$v = v_{0} + \frac{e E _{0} t}{m}$
$λ = \frac{h}{m v} = \frac{h}{m ( v _{0} + \frac{e E _{0}}{m} t )}$
$λ^{'} = \frac{h}{m v _{0} ( 1 + \frac{e E}{m v} t )}$
$λ^{'} = \frac{λ _{0}}{( 1 + \frac{e E _{0}}{m v _{0}} t )}$

Q. An electron (mass m ) with an initial velocity v=v0​i^(v0​>0) is moving in an electric field E=−E0​i^(E0​>0) where E0​ is constant. If at t=0 de Broglie wavelength is λ0​=mvh​, then its de Broglie wavelength after time t is given by

λ0​

λ0​(1+mv0​eE0​t​)

λ0​t

(1+mv0​eE0​t​)λ0​​