In class we talked about white dwarfs, certain cold stars that are stabilized against gravitational collapse by the degeneracy pressure of their electrons. a) Following the notes, carefully re-derive the radius R for which the total energy of the star is minimum. We are assuming constant density. b) Determine the radius, in kilometers, of a white dwarf with the mass of the sun. Assume that Ne = Msun mp) where Z/A is the ratio of the atomic number to atomic mass number, mp = 1.673 x 10-27 kg is the proton mass, and Msun = 1.989 x 1030 kg is the mass of the sun. For a white dwarf, consider ZA 1/2. The mass of the electron is me = 9.109 x 10-31 kg, the gravitational constant is G = 6.674 x 10-11 m kg-1 5-2, and ħ= 1.054 x 10-34 m² kg/s. c) Estimate a characteristic ne under typical conditions inside a white dwarf. Using the result of (b), and assuming a temperature of T = 107 K, evaluate numerically the ratio ETH EF, where Eth is the characteristic thermal energy of an electron in a gas of temperature T (kBT, where kB = 8.62 x 10-5eV/K is the Boltzmann constant), to see that the electrons inside a white dwarf are indeed degenerate.