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An electron (mass m) with an initial vel...

An electron (mass m) with an initial velocity `v=v_(0)hat(i)(v_(0)gt0)` is in an electric field `E=-E_(0)hat(l)(E_(0)="constant"gt0)`. Its de-Broglie wavelength at time t is given by

A

`lamda_0/((1+(eE_0t)/(m v_0)))`

B

`lamda_0(1+(eE_0t)/(m v_0))`

C

`lamda_0`

D

`lamda_0t`.

Text Solution

Verified by Experts

The correct Answer is:
A
Given , initial velocity of electron , `vecv=v_0hati`
The de Broglie wavelength associated with electron is
`lamda_0 =h/(mv_0)`
Force on electron in electric field is
`vecF=-evecE=-e(-E_0hati)=eE_0hati`
Acceleration attained by the electron is
`veca=vecF/m=(eE_0hati)/m`
After time t , velocity of electron will be
`vecv=vecv_0+vecat`
`=v_0hati+((eE_0)/mhati)t`
`=(v_0+(eE_0)/mt)hati=v_0(1+(eE_0)/(mv_0)t)hati`
The de Broglie wavelength associated with the electron at time t is
`lamda=h//p=h/(mv)=h/(m[v_0(1+(eE_0)/(mv_0)t)])`
`=h/(mv_0(1+(eE_0)/(mv_0)t))`
`=lamda_0/((1+(eE_0)/(mv_0))t)`
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