Can Fusion Overcome Gravitational Potential Energy in White Dwarf Explosions?

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SUMMARY

The discussion centers on the explosive fusion process in white dwarf stars, specifically the fusion of carbon into nickel, which releases approximately 280 MeV of energy per fusion event. Participants calculated the total energy released during this process and compared it to the gravitational potential energy using the formula U = -GM²/R. The conclusion reached is that the energy from fusion exceeds the gravitational potential energy, confirming that the explosion can indeed overcome gravitational forces and disperse the star.

PREREQUISITES
  • Understanding of nuclear fusion processes, specifically carbon to nickel fusion.
  • Familiarity with energy calculations in astrophysics, including gravitational potential energy.
  • Knowledge of the equation E = mc² and its application in nuclear energy calculations.
  • Basic grasp of astrophysical concepts related to white dwarf stars.
NEXT STEPS
  • Research the specifics of carbon fusion in stellar environments.
  • Study the implications of energy release in supernova explosions.
  • Learn about the role of gravitational potential energy in stellar evolution.
  • Explore advanced nuclear physics concepts related to fusion efficiency.
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in the mechanics of stellar explosions and nuclear fusion processes in white dwarfs.

leonne
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Homework Statement


The explosive fusion occurs in several steps, but the ultimate result is that carbon
is fused into nickel Assuming that the entire white dwarf
is carbon that fuses to nickel, show that the energy released in the explosion
overcomes the gravitational potential energy, thus blowing apart the star.

Homework Equations


U~-GM2/R

The Attempt at a Solution


Ok so iI found how much energy you get when u fuse carbon to nickel 280Mev. Not sure what to do from here. I found the efficiency to be .0018 and was thinking of using
E(nuclear)=eMc2 Would this be the energy released?
Than I just set the energy released = to the grav potential energy right?
Thanks for the help
 
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The problem statement says that the entire white dwarf is carbon fusing to nickel. How much energy would that release, given that each fusion process releases 280 MeV?

(They're clearly just going for a reasonable/approximation approach, so you're overthinking it)
 
lol always get a reply back after the homework is due. Well I figured it out, it was exacly what i said , but in the end just have to show E is greater then U
 

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