An electron of mass m with an initial velocity →V=V0^i(V0>0) enters an electric field →E=−E0^i(E0=constant >0) at t=0. If λ0 is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is?
λ0(1+eE0mV0t)
λ0t
λ0(1+eE0mV0t)
λ0
A
λ0(1+eE0mV0t)
B
λ0t
C
λ0(1+eE0mV0t)
D
λ0
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Solution
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The diagram will be :-
Initial velocity =V0
∵ Acceleration is constant :-
Final velocity =v=v0+eE0mt
(at time t)
Now, at t=0⇒ de-Broglie wavelength =λ0
⇒λ0=hmv0
Let at time t, de-Broglie wavelength =λ
Then, λ=hmV
=hm(V0+eE0tm)
=hmV0+eE0t
=11/λ0+eE0t/h
=λ.hh+eE0λ0t
=λ01+eEoλ0th
=λ=λ01+(eE0mV0)t
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