# Derive relationship between radioactive constant and half life

1. May 3, 2013

### quantic123

Hi,

I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant.

It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2.

From $A=A_0 e^{-bt}$, just manipulate the exponential: $$A=A_0 e^{-bt}=A_0 2^{\frac{-bt}{\ln(2)}} = A_0 2^{-\frac{t}{t_{1/2}}}$$