JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Modern Physics

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A particle is traveling 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 :

(A) $\frac{1}{16}$ times the mass of $e^{-}$
(B)8 times the mass of $e^{-}$
(C) $\frac{1}{8}$ times the mass of $e^{-}$ ✓ Correct
(D)16 times the mass of $e^{-}$

Answer: (C)

Solution

The de Broglie wavelength is

λ = \frac{h}{m v}

, so

\frac{λ _{p}}{λ _{e}} = \frac{m _{e} v _{e}}{m _{p} v _{p}}

With

v_{p} = 4 v_{e}

and

\frac{λ _{p}}{λ _{e}} = 2

2 = \frac{m _{e} v _{e}}{m _{p} ( 4 v _{e} )} = \frac{m _{e}}{4 m _{p}}

m_{p} = \frac{m _{e}}{8}

. The mass of the particle is

\frac{1}{8}

times the mass of an electron.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option

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