Dual Nature of Matter

JEE Main level, single correct, medium

45 of 200

Question 45 of 200

A proton, a neutron, an electron and an α\alpha-particle have same energy. If λp,λn,λe{\lambda }_{p},{\lambda }_{n},{\lambda }_{e} and λα{\lambda }_{\alpha } are the de Broglie's wavelengths of proton, neutron, electron and α\alpha particle respectively, then choose the correct relation from the following

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Answer: (B) λa<λn<λp<λe{\lambda }_{a}\lt {\lambda }_{n}\lt {\lambda }_{p}\lt {\lambda }_{e}

The de-Broglie wavelength λ=h2m(K.E.)\lambda =\dfrac{h}{\sqrt{2m(K.E.)}}
where, hh and K.E.K.E. are constant
λ∝1m\lambda \propto \dfrac{1}{\sqrt{m}}
m=m= Mass of the particle
Thus, with increasing mass of particle de-Broglie wavelength decreases.
Order of mass me<mp<mn<mα{m}_{e}\lt {m}_{p}\lt {m}_{n}\lt {m}_{\alpha }
Order of de-Broglie wavelength is λa<λn<λp<λe{\lambda }_{a}\lt {\lambda }_{n}\lt {\lambda }_{p}\lt {\lambda }_{e}

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