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What’s the relation between activity and half-life

  • #1
I’m confused because there are two equations:

1) A=λN

2) A=A0exp^-(λt)


If half-life increases, λ decreases, and A decreases according to 1); but,

If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)


Why is this so? Where went wrong? Thanks!
 

Answers and Replies

  • #2
Drakkith
Staff Emeritus
Science Advisor
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If half life increases, λ decreases, hence exp^-(λt) decreases
This doesn't look correct. Given the function ##Y=e^{-x}##,
##Y## should increase if ##x## decreases since ##e^{-x}=\frac{1}{e^x}##. Graphing this equation should immediately show you how the function behaves.

1) A=λN

2) A=A0exp^-(λt)
Hmmm. I think the second equation should be ##N=N_0e^{-λt}##, where ##N## is the number of nuclides remaining after time ##t##.
See this page: https://www.miniphysics.com/activity-half-life-and-decay-constant.html
 
  • #3
This doesn't look correct. Given the function ##Y=e^{-x}##,
##Y## should increase if ##x## decreases since ##e^{-x}=\frac{1}{e^x}##. Graphing this equation should immediately show you how the function behaves.



Hmmm. I think the second equation should be ##N=N_0e^{-λt}##, where ##N## is the number of nuclides remaining after time ##t##.
See this page: https://www.miniphysics.com/activity-half-life-and-decay-constant.html
Thanks!
 

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