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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

Assume:(λ0=hmv0)

A
λ01+eE0tmv0
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B
λ0(1+eE0tmv0)
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C
λ0
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D
λ0t
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Solution

The correct option is A λ01+eE0tmv0
Here, ¯E=E0^i ; initial velocity ¯v=v0^i Force action on electron due to electric field ¯F=(e)(E0^i)=eE0^i
Acceleration produced in the electron, ¯a=¯Fm=eE0m^i
Now, velocity of electron after time t, ¯vt=¯v+¯at=(v0+eE0m)^ior|¯vt|=v0+eE0tm

Now,
λt=hmvt=hm(v0+eE0tm)=hmv0(1+eE0tmv0)

λt=λ0(1+eE0tmv0) (λ0=hmv0)

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