Dual Nature of Matter

JEE Main level, single correct, medium

62 of 200

Question 62 of 200

An electron, a doubly ionized helium ion (He++He^{++}) and proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength λe∗λHe++{\lambda }_{{e}^{*}}{\lambda }_{{He}^{++}} and λp{\lambda }_{p} is :

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Answer: (C) λe>λp>λHe++\lambda_e\gt \lambda_p\gt \lambda_{{He}^{++}}

λ=hmv=h2mk\lambda=\frac{h}{m v}=\frac{h}{\sqrt{2 m k}}
λe:λp:λHe++=1me:1mp:1He++\lambda_{\mathrm{e}}: \lambda_{\mathrm{p}}: \lambda_{{He}^{++}}=\frac{1}{\sqrt{\mathrm{m}_{\mathrm{e}}}}: \frac{1}{\sqrt{\mathrm{m}_{\mathrm{p}}}}: \frac{1}{\sqrt{\mathrm{He}^{++}}}
19.1×10−31:11.6×10−27:14×1.6×10−27=84:2:1\frac{1}{\sqrt{9.1 \times 10^{-31}}}: \frac{1}{\sqrt{1.6 \times 10^{-27}}}: \frac{1}{\sqrt{4 \times 1.6 \times 10^{-27}}}=84: 2: 1

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