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Problem 2.3 The gravitational potential energy of a star is Ugray = 3GM2 5R where M is its mass and R is its radius. 60 CHAPTER 2. STATISTICAL PHYSICS 1. Consider a white dwarf star consisting mostly of carbon. Write down the number of electrons N for this star in terms of its mass. A carbon atom contains 6 electrons. Carbon gas a molar mass of 12 g. There are 6 x 1023 atoms in a mole.] 2. If the star has cooled so that kpT « Ef then the energy of the electrons is Ee = 3NEF/5, and the pressure inside the star is Pe=2E/3V. This pressure tends to make the star expand. However, the gravitational attraction of the carbon atoms towards each other counteracts this expansion. The two forces are in equilibrium when the total energy Etot = Ep + Ugray of the star is a minimum. Find the equilibrium radius of the star if its mass is 1030 kg (half the mass of the sun). Physical constants: G= 6.7 x 10-11 N m² kg-2 ħ= 1.05 x 10-34 Js me = 9.2 x 10-31 kg