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

An electron (mass m) with initial velocity `vecv = v_0 hati + 2v_0 hatj` is in an electric field `vecE = E_0 hatk` . If `lamda_0` is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

A

`(lamda_0 sqrt2)/sqrt(1+(e^2 E^2t^2)/(m^2 v_0^2))`

B

`(lamda_0 sqrt2)/sqrt(2+(e^2 E^2t^2)/(m^2 v_0^2))`

C

`(lamda_0 sqrt2)/sqrt(3+(e^2 E^2t^2)/(m^2 v_0^2))`

D

`(lamda_0 )/sqrt(1+(e^2 E^2t^2)/(5m^2 v_0^2))`

Text Solution

Verified by Experts

The correct Answer is:
D
By de-Broglie hypothesis
`lamda = h/ (mv)`
` lamda_0 = h/(msqrt5 v_0)" ...(1)"`
`lamda' = h/(msqrt(V_0^2 + 4 v_0^2 + ((3R_0t)/m)^2))`
`= h/(msqrt(5 v_0^2 + (e^2 E_0^2 t^2)/m^2))" ...(2)"`
By (1) and (2) `lamda, =lamda_0/sqrt(1+(e^2 E_0^2 t^2)/(5m^2 V_0^2))`
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