Dual Nature of Matter

JEE Main level, single correct, medium

58 of 200

Question 58 of 200

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100V100V. What should nearly be the ratio of their wavelengths ?? (mp=1.00727u,me=0.00055u)\left({m}_{p}=1.00727u,{m}_{e}=0.00055u\right)

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Answer: (D) 43:143:1

λ=hmv=h2mK=h2mqV\lambda =\dfrac{h}{mv}=\dfrac{h}{\sqrt{2mK}}=\dfrac{h}{\sqrt{2mqV}}
λ1λ2=m2m1\dfrac{{\lambda }_{1}}{{\lambda }_{2}}=\sqrt{\dfrac{{m}_{2}}{{m}_{1}}}
λeλp=mpme=1831.4=42.79\dfrac{{\lambda }_{e}}{{\lambda }_{p}}=\sqrt{\dfrac{{m}_{p}}{{m}_{e}}}=\sqrt{1831.4}=42.79

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