JEE Main 2023PhysicsDual Nature of MatterMediumMCQ

JEE Main 2023 — Dual Nature of Matter Question with Solution

JEE Main 2023 (10 Apr Shift 1)

Question

The de Broglie wavelength of a molecule in a gas at room temperature 300 K is λ1. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes

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Show full solutionCorrect option: C
Correct answer
C12λ1

Step-by-step explanation

The root mean squared velocity of a gas is given by 

v=3RTM

⇒v∝T

Let

 T1=300 KT2=600 K

Taking velocity ratios at the given temperatures,

v1v2=T1T2=300600=12

The de Broglie wavelength is given by λ=hmv. So,

λ∝1v

The ratio of the wavelengths is 

λ1λ2=v2v1=21

⇒λ2=12λ1

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About this question

This is a previous-year question from JEE Main 2023, covering the Dual Nature of Matter chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.