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Question

An electron (mass m) with an initial velocity, v=v0 ^i (v0>0) is in an electric field, E=E0 ^i (E0=constant>0) . Its de broglie wavelength at time t is given by (λ0 is the initial wavelength of electron)

A
λ0(1+eE0mv0t)
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B
λ0(1+eE0mv0t)
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C
λ0t
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D
λ0
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Solution

The correct option is A λ0(1+eE0mv0t)
Let λ0=hmv0
Force on electron in electric field F=eE
=e[E0^i]
=eE0^i
Acceleration a=Fm
=eE0^im
Velocity of the electron after time t ,
v=v0^i+(eE0mt)^i
=v0(1+eE0mv0t)^i
|v|=λ0(1+eE0mv0 t)

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