Dual Nature of Matter

JEE Main level, single correct, medium

21 of 200

Question 21 of 200

A proton and an electron have the same de Broglie wavelength. If Kp\mathrm{K}_{\mathrm{p}} and Ke\mathrm{K}_{\mathrm{e}} be the kinetic energies of proton and electron respectively, then choose the correct relation :

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Answer: (B) Kp<Ke\mathrm{K}_{\mathrm{p}} \lt \mathrm{K}_{\mathrm{e}}

De Broglie wavelength of proton \& electron =λ=\lambda
∵λ=hp∴pproton =pelectron ∵KE=p22 m∴KEproton <KEelectron [Kp<Kc]\begin{aligned} & \because \lambda=\frac{\mathrm{h}}{\mathrm{p}} \\ & \therefore \mathrm{p}_{\text {proton }}=\mathrm{p}_{\text {electron }} \\ & \because \mathrm{KE}=\frac{\mathrm{p}^2}{2 \mathrm{~m}} \\ & \therefore \mathrm{KE}_{\text {proton }} \lt \mathrm{KE}_{\text {electron }} \\ & {\left[\mathrm{K}_{\mathrm{p}} \lt \mathrm{K}_{\mathrm{c}}\right]}\end{aligned}

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