Dual Nature of Matter

JEE Main level, single correct, medium

20 of 200

Question 20 of 200

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

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Answer: (A) λα<λp<λe\lambda_\alpha \lt \lambda_{\mathrm{p}} \lt \lambda_{\mathrm{e}}

λDB=hp=h2mk⇒λDBα1m⇒λa<λp<λe\begin{aligned} & \lambda_{\mathrm{DB}}=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mk}}} \\ & \Rightarrow \lambda_{\mathrm{DB}} \alpha \frac{1}{\sqrt{\mathrm{m}}} \\ & \Rightarrow \lambda_{\mathrm{a}} \lt \lambda_{\mathrm{p}} \lt \lambda_{\mathrm{e}}\end{aligned}

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