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An electron of mass m with an initial ve...

An electron of mass `m` with an initial velocity
`vec(v) = v_(0) hat`(i) `(v_(0) gt 0)` enters an electric field
`vec(E ) =- E_(0) hat (i)` `(E_(0) = constant gt 0)` at `t = 0` . If `lambda_(0)` is its de - Broglie wavelength initially, then its de - Broglie wavelength at time `t` is

A

`lambda_(0)t`

B

`lambda_(0)(1+((eE_(0))/(mV_(0))t)`

C

`(lambda_(0))/((1+(eE_(0))/(mV_(0))t)`

D

`lambda_(0)`

Text Solution

Verified by Experts

The correct Answer is:
C
Initial de-Brogile wavelength
`lambda_(0)=(h)/(mV_(0))" "…(i)`

Acceleration of electron
`a=(eE_(0))/(m)`
Velocity after time 't'
`V=(V_(0)+(eE_(0))/(m)t)`
So, `lambda=(h)/(mV)=(h)/(m(V_(0)+(eE_(0))/(m)t))=(h)/(mV_(0)[1+(eE_(0))/(mV_(0))t])=(lambda_(0))/([1+(eE_(0))/(mV_(0))t])" "(ii)`
Divided (ii) by (i) ,
`lambda=(lambda_(0))/([1+(eE_(0))/(mV_(0))t])`
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