What’s the relation between activity and half-life

[Angela Liang]

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!

 

[Drakkith]

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

 

[Angela Liang]

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!