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Question

A particle is travelling, 4 times as fast as an electron. Assuming the ratio of the de-Broglie wavelength of a particle to that of the electron is 2:1, the mass of the particle is


A

1/16 times of mass of electron

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B

1/6 times the mass of electron

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C

1/8 times the mass of electron

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D

8 times the mass of electron

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Solution

The correct option is C

1/8 times the mass of electron


Step 1: Given data

The ratio of the de-Broglie wavelength, λpλe=21 [ λp,λe is wavelength of the particle and the electron respectively]

Velocity of particle, vp=4ve [vp,ve is velocity of the particle and the electron respectively.]

Step 2: Find mass of particle, m

The wavelength is given by

λ=hpλ=hmvλpλe=hmpvphmeveλpλe=mevempvp21=memp×ve4vemp=me8 [Where, p=mv is momentum, h is Planck's constant, mp,me is the mass of the particle and the electron respectively. ]

Hence, optionC is correct.


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