How Do You Calculate Particle Density in a Star Using Electron Energy?

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SUMMARY

The calculation of particle density in a star using electron energy involves using the total energy, which includes both the rest mass energy and the kinetic energy. Specifically, for electrons, the total energy is calculated as rest mass energy (m₀c²) plus the kinetic energy of 0.8 MeV. To determine the minimum density of a neutron star, one must apply the principles of nuclear physics and the equation of state relevant to neutron stars, factoring in the mass-energy equivalence and the specific conditions of neutron degeneracy.

PREREQUISITES
  • Understanding of mass-energy equivalence (E=mc²)
  • Knowledge of electron energy calculations, including rest mass energy and kinetic energy
  • Familiarity with neutron star physics and equations of state
  • Basic principles of nuclear physics and particle density calculations
NEXT STEPS
  • Research the concept of mass-energy equivalence in detail
  • Study the equations of state for neutron stars
  • Learn about the role of electron degeneracy pressure in stellar structures
  • Explore advanced topics in nuclear physics related to particle density calculations
USEFUL FOR

Astronomers, astrophysicists, and students studying stellar physics, particularly those focused on neutron stars and particle density calculations.

tanaygupta2000
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Homework Statement
At what particle density does a completely degenerate electron gas in a star have enough kinetic energy per particle to permit the reaction
p + e + 0.8 MeV -----> n
where p, e and n are proton, electron and neutron respectively. What is the minimum density of the neutron star?
Relevant Equations
The relation between energy E and electron density n is given by :
E = (h^2)/8m (3n/π)^2/3
I am confused whether for electron I have to use rest mass energy (moc2 + 0.8 MeV) or just 0.8 Mev for calculating E.
Also how do I find minimum density of a neutron star using above data ? Please help !
 
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How do I solve such a problem ?
 

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