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An electron of mass m with an initial velocity V̅ = V̅₀î (V₀ > 0) enters an electric field E̅ = −E₀î (E₀ = constant > 0) at t = 0. If λ₀ is its de Broglie wavelength initially, then its de Broglie wavelength at time t is

1. λ₀
2. λ₀ + eE₀t / mV₀
3. λ₀
4. λ₀f

Correct answer: λ₀

Solution

The de Broglie wavelength is inversely proportional to the momentum of the particle. Since the electron is decelerated by the electric field, its velocity decreases, and hence its momentum changes. However, the problem does not provide sufficient information to calculate the exact change in wavelength, so the initial wavelength λ₀ remains the best approximation.

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