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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+ (2^(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
`lambda = (h)/(mv), lambda_0=(h)/(msqrt(10)v_0)`
`lambda. = (h)/(msqrt(v_0^2 + 9v_0^2 + ((2eE_0t)/(m))^2))= (lambda_0)/(sqrt(1 + (2e^2E_0^2t^2)/(5m^2v_0^2)))`
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