Dual Nature of Matter

JEE Main level, single correct, medium

69 of 200

Question 69 of 200

An electron (of mass mm ) and a photon have the same energy EE in the range of a few eVeV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ( c=c= speed of light in vacuum)

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Answer: (C) 1c(E2m)1/2\dfrac{1}{c}{\left(\dfrac{E}{2m}\right)}^{1/2}

λd{\lambda }_{d} for electron =h2mE=\dfrac{h}{\sqrt{2mE}}
λ\lambda for photon =hCE=\dfrac{hC}{E}
Ratio =h2mEEhC=1CE2m=\dfrac{h}{\sqrt{2mE}}\dfrac{E}{hC}=\dfrac{1}{C}\sqrt{\dfrac{E}{2m}}

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