Dual Nature of Matter

JEE Main level, single correct, medium

35 of 200

Question 35 of 200

An α\alpha particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

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Answer: (B) λα<λp<λe{\lambda }_{\alpha }\lt {\lambda }_{p}\lt {\lambda }_{e}

As we know, de-Broglie wavelength is given by,
λ=hp\lambda =\dfrac{h}{p}
and p=2mKp=\sqrt{2mK}
Therefore,
λ=h2mK\lambda =\dfrac{h}{\sqrt{2mK}}
As kinetic energy is the same for all particles,
∴λ∝1m∴\lambda \propto \dfrac{1}{\sqrt{m}}
∵mα>mp>me∵{m}_{\alpha }\gt {m}_{p}\gt {m}_{e}
λe>λp>λα{\lambda }_{e}\gt {\lambda }_{p}\gt {\lambda }_{\alpha }

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