JEE Main 2021PhysicsNuclear PhysicsHardMCQ

JEE Main 2021 — Nuclear Physics Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

At time t=0, a material is composed of two radioactive atoms A and B, where NA(0)=2NB(0) The decay constant of both kind of radioactive atoms is λ. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of NBtNB0 with respect to time t?

Choose an option

Show full solutionCorrect option: C
Correct answer
C

Step-by-step explanation

The rate at which nuclei of B is forming, 

dNBdt=λNA-λNB

dNBdt=2λNB0e-λt-λNB

e-λtdNBdt+λNB=2λNB0e-λteλt

ddtNBe-λt=2λNB0

on integrating above the equation, 
NBeλt=2λtNB+NB0
NBeλt=2λtNB0+NB0

NB=NB1+2λte-λtddtNB=0

-λ1+2λte-λt+2λe-λt=0NBmax at t=12λ

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About this question

This is a previous-year question from JEE Main 2021, covering the Nuclear Physics 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.