An electron of mass m enters a uniform electric field $\vec{E}$ =-E₀k̂ at t=0 with initial velocity $\vec{v}$ =V₀î. If its initial de-Broglie wavelength is λ₀, its de-Broglie wavelength at time t is:
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Question

An electron of mass m enters a uniform electric field $\vec{E}$ =-E₀k̂ at t=0 with initial velocity $\vec{v}$ =V₀î. If its initial de-Broglie wavelength is λ₀, its de-Broglie wavelength at time t is:

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G1 Physics · Accepted Answer

The electron acceleration is along +k̂ with magnitude eE₀/m. Hence |V|=√[V₀²+(eE₀t/m)²]. Since λ=h/(m|V|) and λ₀=h/(mV₀), λ=λ₀/√[1+e²E₀²t²/(m²V₀²)].

An electron of mass m enters a uniform electric field E ⃗ \vec{E} E =-E₀k̂ at t=0 with initial velocity v ⃗ \vec{v} v =V₀î. If its initial de-Broglie wavelength is λ₀, its de-Broglie wavelength at time t is: