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At time t = 0, a material is composed of...

At time t = 0, a material is composed of two radioactive atoms A and B, where `N_(A0) = 2N_(B0)`.
The decay constant of both kind of radioactive atoms is `lamda` . However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of `N_B(t)//N_B(0)` with respect to time t?
[`N_A(0)=`No. of A atoms at t = 0]
[`N_B(0)=` No. of B atoms at t= 0 ]

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C
`A to B , B to C `
`(dN_(B))/(dt) = lambdaN_(A) - lambdaN_(B)`
`(dN_(B))/(dt) =2lambdaN_(B_(0))e^(-lambdat) -lambdaN_(B)`
`e^(-lambdat)((dN_(B))/dt+lambdaN_(B))=2lambdaNB_(0)e^(-lambdat) xx e^(lambdat)`
`d/(dt)(N_(B)e^(lambdat))=2lambdaN_(B_(0)) ` , on integrating
` N_(B)e^(lambdat) = 2lambdatN_(B_(0))+N_(B_(0))`
`N_(B) = N_(B_(0))[1 +2 lambdat]e^(-lambdat)`
`(dN_(B))/dt = 0 " at " -lambda t [1 + 2 lambdat )e^(-lambdat) +2lambdae^(-lambdat) = 0 `
`N_(B_(max)) " at " t = 1/(2lambda)` .
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