Dual Nature of Matter

JEE Main level, single correct, medium

22 of 200

Question 22 of 200

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:
(Assume h=6.63 ×10−34 J s, me=9.0×10−31 kg\times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg} and mp=1836\mathrm{m}_{\mathrm{p}}=1836 times me\mathrm{m}_{\mathrm{e}} )

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Answer: (D) 1: 1836

λ\lambda is same for both
P=hλP=\frac{h}{\lambda} same for both
P=2mK\mathrm{P}=\sqrt{2 \mathrm{mK}}
Hence,
K∝1 m⇒KEpKEe=memp=11836\begin{aligned} & \mathrm{K} \propto \frac{1}{\mathrm{~m}} \\ & \Rightarrow \frac{\mathrm{KE}_{\mathrm{p}}}{\mathrm{KE}_{\mathrm{e}}}=\frac{\mathrm{m}_{\mathrm{e}}}{\mathrm{m}_{\mathrm{p}}}=\frac{1}{1836}\end{aligned}

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