Dual Nature of Matter

JEE Main level, single correct, medium

29 of 200

Question 29 of 200

Proton (P)(P) and electron (e)(e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, mp=1849{m}_{p}=1849 me{m}_{e})

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Answer: (A) 1:11:1

The De Broglie wavelength is λ=hmv\lambda =\dfrac{h}{mv}
The momentum is given by p=mvp=mv
The momentum of proton is pp=mpvp{p}_{p}={m}_{p}{v}_{p}
The momentum of electron is p′=mevep'={m}_{e}{v}_{e}
Since hh is the Planck's constant and it is given that both wavelengths are same, i.e.
λp=λe{\lambda }_{p}={\lambda }_{e}, so pp=p′{p}_{p}=p'.

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