Dual Nature of Matter

JEE Main level, single correct, medium

23 of 200

Question 23 of 200

The de Broglie wavelengths of a proton and an α\alpha particle are λ\lambda and 2λ2\lambda respectively. The ratio of the velocities of proton and α\alpha particle will be :

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Answer: (D) 8:18:1

As we know, de Broglie wavelength is given by, λ=hp=hmv\lambda =\dfrac{h}{p}=\dfrac{h}{mv}
⇒v=hmλ\Rightarrow v=\dfrac{h}{m\lambda }
Therefore,
vpvα=mαmp×λαλp\dfrac{{v}_{p}}{{v}_{\alpha }}=\dfrac{{m}_{\alpha }}{{m}_{p}}\times \dfrac{{\lambda }_{\alpha }}{{\lambda }_{p}}
=4×2=8=4\times 2=8

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