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  • A proton and an  -particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of th

A proton and an \alpha -particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of their de-Broglie wavelength is :

Option: 1

2 : 1


Option: 2

4 : 1


Option: 3

8 : 1


Option: 4

16 : 1


Answers (1)

best_answer

De Broglie wavelength  \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}

\begin{aligned} & \mathrm{m}_\alpha=4 \mathrm{~m} \rightarrow 4 \mathrm{~V} \\ & \mathrm{~m}_{\mathrm{p}}=\mathrm{m} \rightarrow 2 \mathrm{~V} \\ & \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mKE}}} \end{aligned}

\begin{aligned} & \lambda_{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mq}(2 \mathrm{~V})}} \quad \quad \ldots .(1), \quad \lambda_\alpha=\frac{\mathrm{h}}{\sqrt{4 \mathrm{mq}(4 \mathrm{~V})}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mq}(2 \mathrm{~V})}} \times \frac{\sqrt{4 \mathrm{mq}(4 \mathrm{~V})}}{\mathrm{h}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=4 \quad \Rightarrow \quad \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=4: 1 \end{aligned}

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HARSH KANKARIA

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