A proton and an α-particle are accelerated from rest through potentials 2 V and 4 V respectively. The ratio of their de Broglie wavelengths λₚ:λₐ is:
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Question

A proton and an α-particle are accelerated from rest through potentials 2 V and 4 V respectively. The ratio of their de Broglie wavelengths λₚ:λₐ is:

G1 Physics · Accepted Answer

For a charged particle accelerated through potential V, λ = h/√(2mqV) Therefore, λₚ/λₐ = √[(mₐqₐVₐ)/(mₚqₚVₚ)] For an α-particle: mₐ = 4mₚ qₐ = 2qₚ Vₐ = 4 V Vₚ = 2 V Thus, λₚ/λₐ = √[(4 × 2 × 4)/(1 × 1 × 2)] = √16 = 4 Therefore, λₚ : λₐ = 4 : 1 Hence option A follows.