Dual Nature of Matter

JEE Main level, single correct, medium

56 of 200

Question 56 of 200

A particle is travelling 44 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2:1,2:1, the mass of the particle is :-

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Answer: (D) 18\dfrac{1}{8} times the mass of e−{e}^{-}

λ=hp\lambda =\dfrac{h}{p}
λpλe=pepp=mevempVp\dfrac{{\lambda }_{p}}{{\lambda }_{e}}=\dfrac{{p}_{e}}{{p}_{p}}=\dfrac{{m}_{e}{v}_{e}}{{m}_{p}{V}_{p}}
2=memp(ve4ve)2=\dfrac{{m}_{e}}{{m}_{p}}\left(\dfrac{{v}_{e}}{4{v}_{e}}\right)
∴mp=me8∴{m}_{p}=\dfrac{{m}_{e}}{8}

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