An electron with mass ' m ' with an initial velocity (t = 0) v = v₀i (v₀ > 0) enters a magnetic field B = B₀j. If the initial de-Broglie wavelength at t = 0 is λ₀ then its value after time ' t ' would be: (a) (λ₀)/(√(1-(e²B₀²t²)/(m²))) (b) λ₀ (c) λ₀√(1 + (e²B₀²t²)/(m²)) (d) (λ₀)/(√(1+(e²B₀²t²)/(m²)))

Answer: (b). Magnetic force -e( v× B) is perpendicular to v and does no work. Speed and momentum magnitude stay constant. λ = h/(mv) = λ₀ So the answer is (b).

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Matter Waves: de Broglie Wavelength

An electron with mass ' m ' with an initial velocity $(t = 0)\ \vec{v} = v_0\hat{i}\ (v_0 > 0)$ enters a magnetic field $\vec{B} = B_0\hat{j}$ . If the initial de-Broglie wavelength at $t = 0$ is $\lambda_0$ then its value after time ' t ' would be:

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Answer: (b)

Magnetic force $-e(\vec v\times\vec B)$ is perpendicular to $\vec v$ and does no work.
Speed and momentum magnitude stay constant.
$\lambda = h/(mv) = \lambda_0$
So the answer is (b).

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