How Many Daughter Nuclei Exist at Equilibrium in Radioactive Disintegration?

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Homework Help Overview

The discussion revolves around a problem in radioactive disintegration, specifically focusing on the equilibrium state between parent and daughter nuclei. The half-lives of the parent and daughter nuclides are given, and the original poster seeks to determine the number of daughter nuclei at equilibrium based on the number of parent nuclei.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the decay rates of parent and daughter nuclei at equilibrium, questioning how to formulate an equation that reflects this balance. There is also a discussion about the initial and final number of nuclei and whether to use separate equations for each nuclide.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the conditions of equilibrium and the implications for the decay of nuclei. Some guidance has been offered regarding the decay rates, but no consensus has been reached on the correct approach or equations to use.

Contextual Notes

Participants are working under the constraints of the problem's parameters, including the specified half-lives and the number of parent nuclei. There is an emphasis on understanding the equilibrium condition without providing definitive solutions.

Hysteria X
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Homework Statement



In a chain radioactive disintegration,the half-life of the parent and daughter nuclide are 10 years and 25 years respectively.if the disintegration process is at its equilibrium stage with the parent no. of nuclei equal to 5* 10^8, the daughter no. of nuclei will be

Homework Equations


t1/2 = 0.639/λ

n/n0=(1/2)^(t/(t1/2))

n/n0=##e^-λt##

The Attempt at a Solution



t11/2 = 10 years
t21/2 = 25 years
N=No (because its at equilibrium)
→e^-tλ=1
tλ=0??
 
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I would imagine that the processes being in equilibrium means that the number of daughter nuclei that decay is equal to the number of parent nuclei that decay. Can you write an equation from this condition?

Hysteria X said:

Homework Statement



In a chain radioactive disintegration,the half-life of the parent and daughter nuclide are 10 years and 25 years respectively.if the disintegration process is at its equilibrium stage with the parent no. of nuclei equal to 5* 10^8, the daughter no. of nuclei will be

Homework Equations


t1/2 = 0.639/λ

n/n0=(1/2)^(t/(t1/2))

n/n0=##e^-λt##

The Attempt at a Solution



t11/2 = 10 years
t21/2 = 25 years
N=No (because its at equilibrium)
→e^-tλ=1
tλ=0??
 
yes that's what i have writtern n=n0 ?? initial number of nucleus ie parent nuclei = n0 and final number of nuclei ie daughter nuclei=n?
or should i take all together two different equations?
 
No, that's not correct. What's the number of nuclei that decay in a given time?
 

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