Dual Nature of Matter

JEE Main level, single correct, medium

33 of 200

Question 33 of 200

The ratio of de-Broglie wavelength of an α\alpha-particle and a proton accelerated from rest by the same potential is 1m\dfrac{1}{\sqrt{m}} , the value of mm is:

Show answer and solution

Answer: (C) 88

As we know, de Broglie wavelength in terms of energy of particle is given by, λ=12mE\lambda =\dfrac{1}{\sqrt{2mE}}.
Energy gained by proton, E=qVE=qV.
Therefore,
λαλp=h2mαqαVh2mpqpV\dfrac{{\lambda }_{\alpha }}{{\lambda }_{p}}=\dfrac{\dfrac{h}{\sqrt{2{m}_{\alpha }{q}_{\alpha }V}}}{\dfrac{h}{\sqrt{2{m}_{p}{q}_{p}V}}}
⇒λαλp=18\Rightarrow \dfrac{{\lambda }_{\alpha }}{{\lambda }_{p}}=\sqrt{\dfrac{1}{8}}
⇒m=8\Rightarrow m=8

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Photoelectric effect and matter waves simulationDrag the sliders and watch the numbers in this question change.Revise Modern Physics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Dual Nature of Matter (Matter Waves), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.