secular equilibrium

exciting thread title, I know

Can someone please explain secular equilibrium to me? My notes definition says that it means that all the nuclides in a decay series have the same activity. Wikipedia says that it's when the quantity of a radioactive isotope remains constant because its production rate is equal to its decay rate.

For some reason I just can't wrap my head around this. Apparently secular equilibrium can only occur if the half life of the daughter is much shorter than the half life of the parent. But if that's the case, how do you reach equilibrium? Wouldn't the daughter just decay before more daughter material is made? What am I not getting here?

I realized I didn't understand this at all when I couldn't answer the question: "at secular equilibrium, is the number of atoms present larger for the longer-lived isotopes or the shorter-lived isotopes?"

Any help appreciated, I have an exam tomorrow at 10 am :P

ive been thinking of going back to school, but i think what you just wrote motivated me to put it off.

Maybe this example will make it clearer.

In a given second the parent has a 10% chance of decaying (long half life). The daughter has a 50% chance of decaying (short half life). We start with 1000 atoms of parent and no daughters.

Each second, 10% of the parent atoms are converted to daughter atoms, and 50% of the previous seconds daughter atoms decay away.


Time | Number of Parents | Number of daughters

0 | 1000 | 0
1 | 900 | 100
2 | 810 | 140
3 | 729 | 151
4 | 656 | 149
5 | 589 | 142


So even though this is a crappy example you can see that the number of daughter atoms is hovering around the same value. Even though the half life is much shorter for the daughter, there are still so many more parents that there are more parent decays than daughter decays per second (in the beginning). I hope this helps and I hope you get it before your exams :)

Goodluck!

Quote:

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Originally Posted by will641

ive been thinking of going back to school, but i think what you just wrote motivated me to put it off.

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Maybe it will be okay if you don't do a Science degree ...

Quote:

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Originally Posted by Pelion

Maybe this example will make it clearer.

In a given second the parent has a 10% chance of decaying (long half life). The daughter has a 50% chance of decaying (short half life). We start with 1000 atoms of parent and no daughters.

Each second, 10% of the parent atoms are converted to daughter atoms, and 50% of the previous seconds daughter atoms decay away.


Time | Number of Parents | Number of daughters

0 | 1000 | 0
1 | 900 | 100
2 | 810 | 140
3 | 729 | 151
4 | 656 | 149
5 | 589 | 142


So even though this is a crappy example you can see that the number of daughter atoms is hovering around the same value. Even though the half life is much shorter for the daughter, there are still so many more parents that there are more parent decays than daughter decays per second (in the beginning). I hope this helps and I hope you get it before your exams :)

Goodluck!

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THANK YOU! :heart: I read it in the morning before I left for school, and I understand it so much better after looking at your example.