Half-Life Formula: Is It Possible?

[pantheid]

Hi, I have always wondered, is there a known formula that predicts the half life of an atom based on known values (e.g., number of protons and neutrons) rather than observation?

 

[Simon Bridge]

Yes - sort of.
The theory predicts the decay crossections for different modes using the initial and final states of the nucleons.
As a starting point, look up: "Fermi's Golden Rule".

 

[Bill_K]

Hi, I have always wondered, is there a known formula that predicts the half life of an atom based on known values (e.g., number of protons and neutrons) rather than observation?

The half-life of an atom? You mean the half-life of a nucleus, I assume. Naturally a full answer to this question gets very complex, taking up much of a semester course in nuclear physics. Here's the simplest possible answer: it depends primarily on the energy available for the decay.

For beta decay we utilize a function f(Z, E) called the Fermi integral, and in place of the half-life t_1/2 of beta emitters, we study their "comparative lifetimes" ft_1/2. We find that ft values are somewhat the same, and fall into several groups depending on whether the decay is "allowed", "superallowed", "forbidden", etc.

For alpha decays, the variation of ln(t_1/2) versus decay energy results in a linear relation, the Geiger-Nuttall law.

In both cases these results are just first approximations, which can be improved by more detailed theoretical models.