# I Is there a tie between half life and energy of decay?

1. Mar 14, 2016

### Subductionzon

As we all know radioactive isotopes have different half lives and different decay energies. Is there any tie between how long or short the half life is and the amount of energy of decay? I know that it will be a rather complex problem, especially for alpha decay where the mass of the isotope could also figure into the problem

2. Mar 14, 2016

Staff Emeritus
It is a cery complicated thing, as you say. There is a trend towards shorter half-lives for more energetic decays, but this is just one of multiple factors.

3. Mar 14, 2016

### Subductionzon

Thank you. That was what I assumed, but it is nice to have a "reasonable assumption" confirmed. It appears that it is too complicated to represent simply. Thank you for your response.

4. Mar 14, 2016

### e.bar.goum

For alpha decay, it's not too bad an assumption!
https://dl.dropboxusercontent.com/u/34677838/alplot.gif [Broken]

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/alptun.html

This relationship is known as the Geiger-Nuttall law.
https://en.wikipedia.org/wiki/Geiger–Nuttall_law

$\ln \lambda = -a_1 \frac{Z}{\sqrt{E}}+a_2$

This shouldn't be too surprising considering the normal picture of alpha decay - a preformed alpha cluster rattling around in the potential of the nucleus - it has a chance to tunnel through the barrier, and that will be exponentially dependent on energy.

It'll be more complex for other decay modes.

Last edited by a moderator: May 7, 2017