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[Sorry about the long post]
I'm doing an essay where I am exploring whether or not elements were, for the most part, formed under conditions of thermodynamic equilibrium. We know that some element clearly aren't (such as Potassium 40 and uranium which decay radioactivly). I've scoured the web but information on this is suprisingly hard to come by! I'm hoping someone can help!
Basically, I am assuming elements were formed by a simple nuclear build up model thus:
[A-1,Z]+neutron--> [A,Z]
where [A,Z] is an element (or isotope) with mass number A and atomic (proton) number Z. This is plausible because there is no colomb barrier for neutrons to pass through, unlike protons.
If elements WERE formed under conditions of thermodynamic equilibrium, we can use simple Maxwell Boltzmann statistics to work out equilbrium temperatures. (The probability of a particle being in a state Ea is simply exp(-Ea/KT) so we can use the relative abundances of isotope pairs to work out a temperature at which both [A-1,Z] AND [A,Z] are at equilibrium:
Equilbrium Temperature=[tex]\frac{-Dc^{2}}{kln([A-1,Z]/[A,Z]}[/tex]
where
D= Mass Difference = M[A,Z] - {M[A-1,z]+M[neutron]}
k is boltzmann's constant
c is speed of light
and where square brakets [..] now represent the concentration, or relative abudance of the isotope in question.
NOW, on calculating equilibrium temperatures for isotope pairs ([A,Z] and [A-1,Z] of all the elements in the periodic table (please see attached file), I get negative temperatures in some instances! Is there a physical explanation for this?
Furthermore, the equilibrium temperatures seem very high (~10^10 to 10^11 kelvins). As far as I am aware, at such temperatures there is plasma - a "cosmic soup", can there be thermodynamic equilbrium under such conditions?
(if you've got this far, thank you!)
I'm doing an essay where I am exploring whether or not elements were, for the most part, formed under conditions of thermodynamic equilibrium. We know that some element clearly aren't (such as Potassium 40 and uranium which decay radioactivly). I've scoured the web but information on this is suprisingly hard to come by! I'm hoping someone can help!
Basically, I am assuming elements were formed by a simple nuclear build up model thus:
[A-1,Z]+neutron--> [A,Z]
where [A,Z] is an element (or isotope) with mass number A and atomic (proton) number Z. This is plausible because there is no colomb barrier for neutrons to pass through, unlike protons.
If elements WERE formed under conditions of thermodynamic equilibrium, we can use simple Maxwell Boltzmann statistics to work out equilbrium temperatures. (The probability of a particle being in a state Ea is simply exp(-Ea/KT) so we can use the relative abundances of isotope pairs to work out a temperature at which both [A-1,Z] AND [A,Z] are at equilibrium:
Equilbrium Temperature=[tex]\frac{-Dc^{2}}{kln([A-1,Z]/[A,Z]}[/tex]
where
D= Mass Difference = M[A,Z] - {M[A-1,z]+M[neutron]}
k is boltzmann's constant
c is speed of light
and where square brakets [..] now represent the concentration, or relative abudance of the isotope in question.
NOW, on calculating equilibrium temperatures for isotope pairs ([A,Z] and [A-1,Z] of all the elements in the periodic table (please see attached file), I get negative temperatures in some instances! Is there a physical explanation for this?
Furthermore, the equilibrium temperatures seem very high (~10^10 to 10^11 kelvins). As far as I am aware, at such temperatures there is plasma - a "cosmic soup", can there be thermodynamic equilbrium under such conditions?
(if you've got this far, thank you!)
