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An electron (mass m) with initial veloci...

An electron (mass m) with initial velocity `bar(v) = -v_(0)hati + 3v_(0)hatk` is in an electric field `hatE = = 2E_(0)hatj`. If `lamda_(0)` is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

A

`(lamda_(0))/(sqrt(1 + (2e^(2)E_(0)^(2)t^(2))/(5m^(2)v_(0)^(2)))`

B

`(lamda_(0))/(sqrt(2 + (e^(2)E^(2)t^(2))/(m^(2)v_(0)^(2)))`

C

`(lamda_(0))/(sqrt(1 + (e^(2)E^(2)t^(2))/(2m^(2)v_(0)^(2)))`

D

`(lamda_(0))/(sqrt(1 + (e^(2)E_(0)^(2)t^(2))/(5m^(2)v_(0)^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
By de - Broglie hypothesis
`lamda = (h)/(mv), lamda_(0) = (h)/(msqrt(10)v_(0))`
`lamda' = (h)/(msqrt(v_(0)^(2) + 9v_(0)^(2) + ((2eE_(0)t)/(m))^(2))) = (lamda_(0))/(sqrt(1 + (2e^(2)E_(0)^(2)t^(2))/(5m^(2)V_(0)^(2))`
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