Q80 / 90 · JEE Main 2021 (26 Aug Shift 2) · Physics

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?

  • A
    Figure
  • B
    Figure
  • Correct answer
    C
    Figure
  • D
    Figure

Solution

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

Figure

Hence, the correct answer is option: 'C'.

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