An electron and a proton are each accelerated from rest through the same potential difference V. Their de Broglie wavelengths are λₑ and λₚ, and their masses are mₑ and mₚ. Neglect relativistic effects. What is λₑ / λₚ?
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Question

An electron and a proton are each accelerated from rest through the same potential difference V. Their de Broglie wavelengths are λₑ and λₚ, and their masses are mₑ and mₚ. Neglect relativistic effects. What is λₑ / λₚ?

Options

G1 Physics · Accepted Answer

For a particle of charge magnitude e accelerated from rest through potential difference V, K = eV. Its momentum is p = √(2meV). Therefore the de Broglie wavelength is λ = h ÷ p = h ÷ √(2meV). For the same accelerating potential and the same charge magnitude, λ ∝ 1 ÷ √m. Hence, λₑ ÷ λₚ = √(mₚ ÷ mₑ). Correct option: A.