Stars similar to our sun eventually become white dwarfs, in which the hydrogen and helium have fused to form carbon and oxygen. The star has collapsed to a much smaller radius, which is why it is described as a “dwarf.” The electrons are not bound to the nuclei and form a degenerate Fermi gas within the white dwarf. Consider a white dwarf with a mass equal to the sun’s mass (1.99 x 1030 kg) but a radius of only 6.96 x 106 m, which is just 1% of the sun’s present radius. (a) If the white dwarf consists of equal parts carbon and oxygen, how many electrons are present? (b) What is the number density of electrons? (c) Find the Fermi energy of the electrons (in units of eV) and comment on the result.
Stars similar to our sun eventually become white dwarfs, in which the hydrogen and helium have fused to form carbon and oxygen. The star has collapsed to a much smaller radius, which is why it is described as a “dwarf.” The electrons are not bound to the nuclei and form a degenerate Fermi gas within the white dwarf. Consider a white dwarf with a mass equal to the sun’s mass (1.99 x 1030 kg) but a radius of only 6.96 x 106 m, which is just 1% of the sun’s present radius. (a) If the white dwarf consists of equal parts carbon and oxygen, how many electrons are present? (b) What is the number density of electrons? (c) Find the Fermi energy of the electrons (in units of eV) and comment on the result.
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