# What’s the relation between activity and half-life

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
Staff Emeritus
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##.

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##.