next up previous
Next: Exercise Up: Problem 1: Radioactive Decay Previous: Problem 1: Radioactive Decay

Preliminary remarks

Radioactive decay is a typical example to which the exponential decay model can be applied. In Eq. (2), y represent the mass (in grams) of an isotope, y0 and k are constants determining from initial conditions: y0 is the mass present originally, and k is the decay constant.

k is often specified in terms of an empirical parameter, the half-life of the isotope. The half-life $\tau$ of a sample of a radioactive isotope is the time required for half of the atoms of that sample to decay. The half-lives of some common radioactive isotopes are as follows:


Uranium (U-238) 4,510,000,000 years  
Plutonium (Pu-239) 24,360 years  
Carbon (C-14) 5,730 years  
Einsteinium (Es-254) 270 days  
Nobelium (No-257) 23 sec  


The relationship between k and $\tau$ is set up from the condition actually saying that the sample of y0 grams will contain only $\displaystyle\frac{1}{2}y_0$ grams after the time $\tau$, so that, referring (2):
\begin{maplelatex} \begin{displaymath} \displaystyle\frac{1}{2} = e^{-k\tau}\end{displaymath}\end{maplelatex}
and therefore:
\begin{maplelatex} \begin{displaymath} \tau = \displaystyle\frac{\ln 2}{k }.\end{displaymath}\end{maplelatex}



next up previous
Next: Exercise Up: Problem 1: Radioactive Decay Previous: Problem 1: Radioactive Decay

Christine M Palmer
9/23/1998