Dual Nature of Matter

JEE Main level, numerical answer, medium

50 of 200

Question 50 of 200

A particle of mass 9.1×10−31kg9.1\times {10}^{-31}kg travels in a medium with a speed of 106ms−1{10}^{6}m{s}^{-1} and a photon of radiation of linear momentum 10−27kgms−1{10}^{-27}kgm{s}^{-1} travels in a vacuum. The wavelength of the photon is ____ times the wavelength of the particle.

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Answer: 910

For photon λ1=hP=6.6×10−3410−27{\lambda }_{1}=\dfrac{h}{P}=\dfrac{6.6\times {10}^{-34}}{{10}^{-27}}
For particle λ2=hmv=6.6×10−349.1×10−31×106{\lambda }_{2}=\dfrac{h}{mv}=\dfrac{6.6\times {10}^{-34}}{9.1\times {10}^{-31}\times {10}^{6}}
∴λ1λ2=910∴\dfrac{{\lambda }_{1}}{{\lambda }_{2}}=910

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