Question

3. A simple model of a Neutron star is an ideal gas of neutrons (each with spin 1/2 in units of h). Aside from the kinetic energy of the neutrons, one must consider the gravitational energy, which for a homogeneous star of mass M and radius R, is 3GM2 5R where G 6.67 x 10-11m3kg-'s-2 is the universal gravitational constant (i) We suppose in this problem that the Fermi temperature is large enough for T0 What general condition determines the equilibrium state? (ii) Derive an expression for the equilibrium radius of the star for the non-relativistic case where the single particle energyp/(2m). (ii) Show that in the relativistic case, where+ m*ct, equilibrium is only possible if the mass of the star is smaller than a critical value M (iv) Can the sun (mass 2 x 1030 kg) evolve into a Neutron star? If yes, how would its radius compare to its present nadius of 70,00km?

Answer 1

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