An α -particle and a proton are accelerated from rest by a potential difference of 100 ~V . After this, their de Broglie wavelengths are λ_α and λ_p respectively. The ratio (λ_p)/(λ_α) , to the nearest integer, is

Correct answer: 0 aligned λ& =(h)/(P)= h 2 q q V m or λ 1 q m (λ_p)/(λ_α)& = (q_α)/(q_p) · m_ m_p = ((2)(4))/((1)(1)) =2.828 aligned The nearest integer is 3 . answer is 3 .

JEE Advanced 2010Paper 1

Exam: JEE Advanced
Year: 2010
Paper: Paper 1
Subject: Physics
Chapter: Dual Nature of Matter

JEE Advanced 2010 · Paper 1 · Physics · Dual Nature of Matter

An α -particle and a proton are accelerated from rest by a...

\alpha

-particle and a proton are accelerated from rest by a potential difference of

100 \mathrm{~V}

. After this, their de Broglie wavelengths are

\lambda_\alpha

and

\lambda_p

respectively. The ratio

\frac{\lambda_p}{\lambda_\alpha}

, to the nearest integer, is

Correct answer

Step-by-step solution

\begin{aligned} \lambda& =\frac{h}{P}=\frac{h}{\sqrt{2 q q V m}} \text{ or } \lambda \propto \frac{1}{\sqrt{q m}}\\ \frac{\lambda_p}{\lambda_\alpha}& =\sqrt{\frac{q_\alpha}{q_p} \cdot \frac{m_{\propto}}{m_p}}=\sqrt{\frac{(2)(4)}{(1)(1)}}=2.828 \end{aligned}

The nearest integer is 3 .\therefore$ answer is 3 .

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