Dual Nature of Matter

JEE Main level, single correct, medium

59 of 200

Question 59 of 200

An electron of mass me{m}_{e} and a proton of mass mp=1836me{m}_{p}=1836{m}_{e} are moving with the same speed. The ratio of their de Broglie wavelength λelectronλproton\dfrac{{\lambda }_{electron}}{{\lambda }_{proton}} will be :

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Answer: (A) 18361836

Given mass of electron =me={m}_{e}
Mass of proton =mp={m}_{p}
∴∴ given mp=1836me{m}_{p}=1836{m}_{e}
From de-Broglie wavelength
λ=hp=hmv\lambda =\dfrac{h}{p}=\dfrac{h}{mv}
λeλp=mpme\dfrac{{\lambda }_{e}}{{\lambda }_{p}}=\dfrac{{m}_{p}}{{m}_{e}}
=1836meme=\dfrac{1836{m}_{e}}{{m}_{e}}
λeλp=1836\dfrac{{\lambda }_{e}}{{\lambda }_{p}}=1836

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