Dual Nature of Matter

JEE Main level, single correct, medium

31 of 200

Question 31 of 200

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ\lambda. An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ\lambda. The ratio of kinetic energy of proton and that of alpha particle is :

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Answer: (B) 4:14:1

As we know, de Broglie wavelength is given by,
λ=hp\lambda =\dfrac{h}{p}
Now kinetic energy can be written as,
K=12mv2=p22m=h22mλ2K=\dfrac{1}{2}m{v}^{2}=\dfrac{{p}^{2}}{2m}=\dfrac{{h}^{2}}{2m{\lambda }^{2}}
Therefore,
K∝1mK\propto \dfrac{1}{m}
Hence, required ratio
KpKα=mαmp=4⇒mα:mp=4:1\dfrac{{K}_{p}}{{K}_{\alpha }}=\dfrac{{m}_{\alpha }}{{m}_{p}}=4 \Rightarrow {m}_{\alpha }:{m}_{p}=4:1

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