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)
λ0⎛⎝1+eE0tmv0⎞⎠
λ0(1+eE0tmv0)
λ0
λ0t
A
λ0(1+eE0tmv0)
B
λ0t
C
λ0
D
λ0⎛⎝1+eE0tmv0⎞⎠
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Solution
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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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