Final answer:
To estimate the number of electrons in the Sun, one can calculate the mass of hydrogen (75% of the Sun's mass) and then divide by the mass of one hydrogen atom. The Fermi energy of the electrons in a white dwarf, their relativistic nature, and whether the gases in the star are degenerate at a given temperature are determined through principles of quantum mechanics and statistical mechanics.
Step-by-step explanation:
The question is asking for an estimate of the number of electrons in the Sun, given that it is mainly composed of atomic hydrogen (which implies that each atom contributes one electron), and then to determine the Fermi energy of the electrons in a white dwarf star of one solar mass and a radius of 2×107 m. The part of the question regarding whether the electrons and nucleons in the star are degenerate if the temperature is 107 K also pertains to states of matter in extreme astrophysical conditions.
To estimate the number of electrons in the Sun, we can assume that the Sun is composed of about 75% hydrogen by mass. Since the mass of the Sun is 2.0×1030 kg, the mass of hydrogen in the Sun would be 1.5×1030 kg. Considering that the mass of a hydrogen atom is approximately 1.67×10-27 kg, we can estimate the number of hydrogen atoms and, hence, electrons in the Sun by dividing the total mass of hydrogen by the mass of one hydrogen atom.