Element synthesis in stars
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Exercise:
Some stars in a later stage of evolution may to fuse two isotopeC nuclei o one isotopeMg nucleus. abcliste abc How much energy would be released in such a reaction? abc What kinetic energy must two carbon nuclei each have when far apart if they can then approach each other within pq.fm center to center? abc Approximately what temperature would this require? abcliste
Solution:
abcliste abc The released energy can be obtained from the mass difference of the reaction: Delta m pq.u- pq.u pq.u. Due to Einstein's energy-mass-equivalence this mass contains the energy E Delta m c^ pq.MeV. abc The velocity of the two carbon-atoms needs to exceed the electrical potential; the law of energy conservation then says: Ekin Epot frac mv^ fracpivarepsilon_fracq^r v^ fracpivarepsilon_fracq^mr fracpivarepsilon_frac pq.C^pqu r pq.emqpsq v pq.e abc The temeprature particles need to have this velocity in average is: Ekin frac kT frac mv^ frac kT mv^ kT T fracmv^k pq.eK. abcliste
Some stars in a later stage of evolution may to fuse two isotopeC nuclei o one isotopeMg nucleus. abcliste abc How much energy would be released in such a reaction? abc What kinetic energy must two carbon nuclei each have when far apart if they can then approach each other within pq.fm center to center? abc Approximately what temperature would this require? abcliste
Solution:
abcliste abc The released energy can be obtained from the mass difference of the reaction: Delta m pq.u- pq.u pq.u. Due to Einstein's energy-mass-equivalence this mass contains the energy E Delta m c^ pq.MeV. abc The velocity of the two carbon-atoms needs to exceed the electrical potential; the law of energy conservation then says: Ekin Epot frac mv^ fracpivarepsilon_fracq^r v^ fracpivarepsilon_fracq^mr fracpivarepsilon_frac pq.C^pqu r pq.emqpsq v pq.e abc The temeprature particles need to have this velocity in average is: Ekin frac kT frac mv^ frac kT mv^ kT T fracmv^k pq.eK. abcliste