Question

A proton and an ∝-particle are passed through same potential difference. If their initial velocity is zero, the ratio of their de Broglie's wavelength after getting accelerated is…… 

(A) 1:1 

(B) 1:2 

(C) 2:1 

(D) 2√2:1

Answer 1

The correct option is (D) 2√2:1.

Explanation:

λ = (h/p) = {h / (√(2meV))}

Given: Potential is same 

Hence

λ ∝ {1 / (√me)}

where m is mass and e is charge

Let mass of charge on proton be m_p and e_p respectively. Mass & charge of ∝ particle m_∝ and e_∝

hence m_∝ = 4m_p

e_∝ = 2e_p

∴ (λ_p / λ_∝) = √{(m_∝ e_∝) / (m_p e_p)}

∴ (λ_p / λ_∝) = √({4m_p / m_p} × {2e_p / e_p})

∴ (λ_p / λ_∝) = √8

∴ (λ_p / λ_∝) = [{2√2} / 1]