An electron of mass m with initial velocity v₀ along +x enters a uniform magnetic field B₀ along +y. If its initial de Broglie wavelength is λ₀, its de Broglie wavelength after time t is:
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Question

An electron of mass m with initial velocity v₀ along +x enters a uniform magnetic field B₀ along +y. If its initial de Broglie wavelength is λ₀, its de Broglie wavelength after time t is:

G1 Physics · Accepted Answer

The magnetic force is F = q(v×B). At every instant the magnetic force is perpendicular to the particle velocity. Hence magnetic force does no work: W = 0. Therefore the electron's kinetic energy and speed remain constant. De Broglie wavelength is λ = h/p = h/(mv). Since v remains constant, momentum magnitude remains constant and so does λ. Thus λ(t) = λ₀. Correct option: A.