A proton and an α-particle both start from rest. The proton is accelerated through 800 V. The α-particle is to be accelerated through a potential difference such that its de Broglie wavelength is exactly equal to that of the proton. Take m(α) = 4mₚ and q(α) = 2e. If the required α-particle accelerating potential is N V, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

A proton and an α-particle both start from rest. The proton is accelerated through 800 V. The α-particle is to be accelerated through a potential difference such that its de Broglie wavelength is exactly equal to that of the proton. Take m(α) = 4mₚ and q(α) = 2e. If the required α-particle accelerating potential is N V, find N.

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

G1 Physics · Accepted Answer

Equal wavelengths mean equal momentum magnitudes. For acceleration from rest, p² = 2mqV. Therefore equal momentum requires mₚ(e)(800) = [4mₚ](2e)V(α). Cancel mₚ and e: 800 = 8V(α). Hence, V(α) = 100 V. Therefore N = 100.