Dual Nature of Matter

JEE Main level, single correct, medium

38 of 200

Question 38 of 200

The equation λ=1.227xnm\lambda =\dfrac{1.227}{x}nm can be used to find the de-Broglie wavelength of an electron. In this equation xx stands for :
Where,
m=m= mass of electron
P=P= momentum of electron
K=K= Kinetic energy of electron
V=V= Accelerating potential in volts for electron

Show answer and solution

Answer: (D) V\sqrt{V}

The de-Broglie's wavelength is given by λ=hmv\lambda =\dfrac{h}{mv}, where, hh is Planck's constant and vv is velocity.
Using relation between momentum and kinetic energy, we have λ=h2m(KE)\lambda =\dfrac{h}{\sqrt{2m\left(KE\right)}}
Here, kinetic energy of electron is stated as KE=qVKE=qV.
Then, we have λ=h2mqV\lambda =\dfrac{h}{\sqrt{2mqV}}
Putting the values of m=9.1×10−31kgandq=1.62×10−19Cm=9.1\times {10}^{-31}kgandq=1.62\times {10}^{-19}C of electron
We get, λ=1.22Vnm\lambda =\dfrac{1.22}{\sqrt{V}}nm.
So, xx stand for V\sqrt{V}.

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.