A charged particle moves perpendicular to a uniform magnetic field B in a circular path of radius r, and its de Broglie wavelength is λ. Another particle with the same charge magnitude moves in the same magnetic field in a circular path of radius 3r. If the second particle's de Broglie wavelength is λ ÷ N, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

A charged particle moves perpendicular to a uniform magnetic field B in a circular path of radius r, and its de Broglie wavelength is λ. Another particle with the same charge magnitude moves in the same magnetic field in a circular path of radius 3r. If the second particle's de Broglie wavelength is λ ÷ N, find N.

Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light

G1 Physics · Accepted Answer

For circular motion in a uniform magnetic field, p = qBr. Therefore, λ = h ÷ p = h ÷ (qBr). For fixed q and B, λ is inversely proportional to r. If the radius becomes 3r, λ₂ = λ₁ ÷ 3. Hence N = 3.