Can we predict element decay using Quantum mechanics?

[physics_head]

Is it possible create a quantum mechanics simulation to predict what the half life of an element will be, say C-14?

I know one way to figure an element's half life is to get a bunch of atoms(a really big number of them), wait for some time to pass, and count how many atoms decayed, thus the half life would be deduced.

But I am thinking we wouldn't need to perform such experiments, couldn't we just use what we know about quantum mechanics and physics to predict what the half life of an unstable element will be?

 

[elduderino]

No. Decay constants are almost always empirically known. Infact, the elegant law $$N = N_0 e^{ - \lambda t}$$ is hard to arrive at through quantum mechanics. Merzbacher (the book) describes that this law is arrived at only through "delicate approximations".

 

[elduderino]

PS: why are my edits not visible.. it doesn't show my correction of the minus sign in the exponential decay formula i poster?

 

[jtbell]

Hit the "refresh" button on your browser, to see the changes you made in your LaTeX.

 

[Vanadium 50]

I disagree - there are decays one can predict with rather good accuracy - in particular beta decays with minimal nuclear effects. For example, I just calculated the half-life of tritium to be 12.8 years. The measurement is around 12.4.

 

[elduderino]

What did you do?

 

[Vanadium 50]

I used the fact that weak decays scale as Q⁵ and the half-life of the neutron.

 

[elduderino]

ahh.. but the knowing the half life!

 

[diazona]

Well, in the current state of physics something has to be measured. We don't have a theory that produces all of physics without having any empirical parameters (although a lot of people are trying). It's just a question of whether you measure the half-life you want directly, or measure something else that let's you calculate the half-life from it.

 

[map19]

What makes an individual atom decay ?
I've seen the suggestion that it is energy 'borrowed' from the zero-point vacuum energy, which would, in turn, depend on energy/time uncertainty.

 

[physics_head]

It seems to me that we should be able to predict the half life of an unstable element. The "cause" of how long on average it takes for an atom to decay should depend on what is going on on the quantum scale within the atom. We know how quantum mechanics works on that scale, we know what kind of atome we are dealing with, therefore it seems to me a good old computer simulation could be conducted to get an extremely accurate estimate of the half life of the simulated atom in question. If the simulation is realistic, then the result should match reality. right?...

 

[Vanadium 50]

ahh.. but the knowing the half life!

That's not a sentence, so I don't know what you are trying to say. If you are arguing that I need to put one half-life into compute another one, of course - there needs to be some sort of data input to the calculation so one knows the absolute strength of the weak force.

 

[elduderino]

$$t_{1/2} = \frac {0.693}{\lambda}$$

in other words, knowing the half life is knowing $$\lambda$$ this is what I wanted to say. I have been anwered, though I'm still not aware of the details, as physics_head wrote..

It seems to me that we should be able to predict the half life of an unstable element. The "cause" of how long on average it takes for an atom to decay should depend on what is going on on the quantum scale within the atom. We know how quantum mechanics works on that scale, we know what kind of atome we are dealing with, therefore it seems to me a good old computer simulation could be conducted to get an extremely accurate estimate of the half life of the simulated atom in question. If the simulation is realistic, then the result should match reality. right?...

Im not an expert here, but from what I've understood, this is one of the departures for the Bohmian interpretaion. Going by the copenhagen dictum, it is not possible to compute the half life of an unstable nucleus, given its physical parameters like atomic mass, etc.. (though the half life is mostly unique for a nuclei of a specific atomic mass)

I'd love to be cleared up here.