Question

An electron (mass $m$ ) with an initial velocity $\overrightarrow{ v }= v _0 \hat{ i }\left( v _0>0\right)$ is moving in an electric field $\overrightarrow{ E }=- E _0 \hat{ i }\left( E _0>0\right)$ where $E _0$ is constant. If at $t =0$ de Broglie wavelength is $\lambda_0=\frac{ h }{ mv }$, then its de Broglie wavelength after time $t$ is given by

• A. $\lambda_0$
• B. $\lambda_0\left(1+\frac{ eE _0 t }{ mv _0}\right)$
• C. $\lambda_0 t$
• D. $\frac{\lambda_0}{\left(1+\frac{ eE _0 t }{ mv _0}\right)}$

Answer 1

Answer: (D)

$E =- E _0 \hat{ i } $
$ \lambda_0=\frac{ h }{ mv _0} $
$ v = v _0+\frac{ e E _0 t }{ m } $
$ \lambda=\frac{ h }{ mv }=\frac{ h }{ m \left( v _0+\frac{ eE _0}{ m } t \right)} $
$ \lambda^{\prime}=\frac{ h }{ mv _0\left(1+\frac{ eE }{ mv } t \right)}$
$ \lambda^{\prime}=\frac{\lambda_0}{\left(1+\frac{ eE _0}{ mv _0} t \right)}$