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JEE Main 202118 MarchMorning Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Morning Shift
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2021 · 18 March · Morning Shift · Physics · Dual Nature of Matter

A particle is travelling 4 times as fast as an electron. Assuming...

A particle is travelling

4

times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is

2: 1,

the mass of the particle is :-

Options

A $\dfrac{1}{16}$ times the mass of ${e}^{-}$
B $8$ times the mass of $e -$
C $16$ times the mass of ${e}^{-}$
D $\dfrac{1}{8}$ times the mass of ${e}^{-}$

Correct answer

D. $\dfrac{1}{8}$ times the mass of ${e}^{-}$

Step-by-step solution

\lambda = \dfrac{h}{p}

\dfrac{{\lambda}_{p}}{{\lambda}_{e}} = \dfrac{{p}_{e}}{{p}_{p}} = \dfrac{{m}_{e}{v}_{e}}{{m}_{p}{V}_{p}}

2 = \dfrac{{m}_{e}}{{m}_{p}}\left(\dfrac{{v}_{e}}{4{v}_{e}}\right)

∴ {m}_{p} = \dfrac{{m}_{e}}{8}

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