A proton and a deuteron, each carrying charge +e, start from rest and are accelerated through the same potential difference. Take the deuteron mass to be twice the proton mass. What is the ratio of their de Broglie wavelengths λₚ:λ(d)?
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Question

A proton and a deuteron, each carrying charge +e, start from rest and are accelerated through the same potential difference. Take the deuteron mass to be twice the proton mass. What is the ratio of their de Broglie wavelengths λₚ:λ(d)?

Options

G1 Physics · Accepted Answer

For a particle accelerated from rest through potential V, λ = h ÷ √(2mqV). The proton and deuteron have the same charge magnitude and are accelerated through the same potential, so λ is inversely proportional to √m. Thus, λₚ ÷ λ(d) = √[m(d) ÷ mₚ] = √2. Therefore, λₚ:λ(d) = √2:1. Correct option: B.