Dual Nature of Matter

JEE Main level, single correct, medium

43 of 200

Question 43 of 200

An α\alpha particle and a carbon 1212 atom has same kinetic energy KK. The ratio of their de-Broglie wavelengths (λα:λC12)\left({\lambda }_{\alpha }:{\lambda }_{C12}\right) is

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Answer: (A) 3:1\sqrt{3}:1

De-Broglie wavelength is stated as λ=hp=h2mK\lambda =\dfrac{h}{p}=\dfrac{h}{\sqrt{2mK}}, where, KK is kinetic energy and mm is mass.
Here, (K)α=(K)C‐12{\left(K\right)}_{\alpha }={\left(K\right)}_{C‐12}.
Now, the ratio λαλC12=12m4m=3:1\dfrac{{\lambda }_{\alpha }}{{\lambda }_{C12}}=\dfrac{\sqrt{12m}}{\sqrt{4m}}=\sqrt{3}:1

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