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JEE Main 202122 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
22 July
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2021 · 22 July · Morning Shift · Physics · Dual Nature of Matter

An electron of mass m _ e and a proton of mass m _ P are...

An electron of mass me{m}_{e} and a proton of mass mP{m}_{P} are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

Options

  1. AmPme\dfrac{{m}_{P}}{{m}_{e}}
  2. B11
  3. Cmpme\sqrt{\dfrac{{m}_{p}}{{m}_{e}}}
  4. Dmemp\dfrac{{m}_{e}}{{m}_{p}}

Correct answer

C. mpme\sqrt{\dfrac{{m}_{p}}{{m}_{e}}}

Step-by-step solution

KE=e\DeltaVKE = e\DeltaV
λe=h2me(e\DeltaV){\lambda}_{e} = \dfrac{h}{\sqrt{2{m}_{e} ( e\DeltaV )}}
λp=h2mp(e\DeltaV){\lambda}_{p} = \dfrac{h}{\sqrt{2{m}_{p} ( e\DeltaV )}}

⇒λeλp=mpme⇒ \dfrac{{\lambda}_{e}}{{\lambda}_{p}} = \sqrt{\dfrac{{m}_{p}}{{m}_{e}}}

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