Consider a white dwarf of mass M and radius R. Let the electrons be degenerate but non-
Question:
Consider a white dwarf of mass M and radius R. Let the electrons be degenerate but non- relativistic; the protons are non-degenerate.
(a) Show that the order of magnitude of the gravitational self-energy is – GM2/R, where G is the gravitational constant. (If the mass density is constant within the sphere of radius R, the exact potential energy is – 3GM2/5R).
(b) Show that the order of magnitude of the kinetic energy of the electrons in the ground state is
Where m is the mass of an electron and MH is the mass of a proton.
(c) Show that if the gravitational and kinetic energies are of the same order of magnitude (as required by the virial theorem of mechanics), M1/3 R ≈ 1020 g1/3 cm.
(d) If the mass is equal to that of the Sun (2 x 1033 g), what is the density of the white dwarf?
(e) It is believed that pulsars are stars composed of a cold degenerate gas of neutrons. Show that for a neutron star M 1/3 R ≈ 1017 g1/3 cm. What is the value of the radius for a neutron star with a mass equal to that of the Sun? Express the result in km.
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