Dual Nature of Matter

JEE Main level, single correct, medium

74 of 200

Question 74 of 200

A particle AA of mass mm and charge qq is accelerated by a potential difference of 50V.50V. Another particle BB of mass 4m4m and charge qq is accelerated by a potential difference of 2500V.2500V. The ratio of de-Broglie wavelengths λAλB\dfrac{{\lambda }_{A}}{{\lambda }_{B}} is close to:

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Answer: (D) 14.1414.14

de-Broglie wavelength λ=hρ\lambda =\dfrac{h}{\rho }

=h2meV=\dfrac{h}{\sqrt{2meV}}

λAλB=4m×2500m×50\dfrac{{\lambda }_{A}}{{\lambda }_{B}}=\sqrt{\dfrac{4m\times 2500}{m\times 50}}

=2×52=2\times 5\sqrt{2}

=14.14=14.14

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